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HP 12C, User Manual

The HP 12C calculator boasts a myriad of financial applications, making it an essential tool for professionals. Unlock the device's full potential with the comprehensive user manual, available for free download from manualshive.com. Explore its features, improve efficiency, and master complex calculations with ease through this invaluable manual.

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Section 13: Investment Analysis  195

 

 

File name: HP 12c Pt Converted_user's guide_English_HDP0F123E02_080207 

Page: 201 of 281   

Printed Date: 

{

  2007/8/2Dimension: 14.8 cm x 21 cm 

 

Modified Internal Rate of Return 

The traditional Internal Rate of Return (

IRR

) technique has several drawbacks which 

hamper its usefulness in some investment applications. The technique implicitly 

assumes that all cash flows are either reinvested or discounted at the computed 
yield rate. This assumption is financially reasonable as long as the rate is within a 

realistic borrowing and lending range (for example, 10% to 20%). When the 

IRR

 

becomes significantly greater or smaller, the assumption becomes less valid and 
the resulting value less sound as an investment measure. 

IRR

 also is limited by the number of times the sign of the cash flow changes 

(positive to negative or vice versa). For every change of sign, the 

IRR

 solution has 

the potential for an additional answer. The cash flow sequence in the example that 
follows has three sign changes and hence up to three potential internal rates of 

return. This particular example has three positive real answers: 1.86, 14.35, and 

29. Although mathematically sound, multiple answers probably are meaningless 
as an investment measure. 
This Modified Internal Rate of Return procedure (

MIRR

) is one of several 

IRR

 

alternatives which avoids the drawbacks of the traditional 

IRR

 technique. The 

procedure eliminates the sign change problem and the reinvestment (or 
discounting) assumption by utilizing user stipulated reinvestment and borrowing 

rates. 
Negative cash flows are discounted at a safe rate that reflects the return on an 
investment in a liquid account. The figure generally used is a short-term security 

(T-Bill) or bank passbook rate. 
Positive cash flows are reinvested at a reinvestment rate which reflects the return on 

an investment of comparable risk. An average return rate on recent market 
investments might be used. 
The steps in the procedure are: 

1.  Calculate the future value of the positive cash flows (

NFV

) at the reinvestment 

rate. 

2.  Calculate the present value of the negative cash flows (

NPV

) at the safe rate. 

3. Knowing 

n

, 

PV

, and 

FV

, solve for 

i

. 

Summary of Contents for 12C

Page 1: ...HP 12c Platinum Financial Calculator User s guide H Edition 5 HP part number F2231AA 90001 ...

Page 2: ...HEWLETT PACKARD CO SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING PERFORMANCE OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN 1981 82 1999 2002 2005 2006 07 Hewlett Packard Development Company L P Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company exc...

Page 3: ...orage registers memories z Section 2 tells you how to use the percentage and calendar functions z Section 3 tells you how to use the simple interest compound interest and amortization functions z Section 4 tells you how to do discounted cash flow analysis bond and depreciation calculations z Section 5 tells you about miscellaneous operating features such as Continuous Memory the display and specia...

Page 4: ...ulation methods in the United Kingdom than in the United States Refer to Appendix G for more information For More Solutions to Financial Problems In addition to the specialized solutions found in Sections 12 through 16 of this handbook many more are available in the optional HP 12c Platinum Solutions Handbook Included are solutions to problems in lending forecasting pricing statistics savings inve...

Page 5: ...he CLEAR Keys 19 Undo Operation 20 The RPN and ALG Keys 20 Simple Arithmetic Calculations in RPN Mode 21 Simple Arithmetic Calculations in ALG Mode 22 Chain Calculations in RPN Mode 23 Chain Calculations in ALG Mode 26 Parentheses Calculations 26 Storage Registers 27 Storing and Recalling Numbers 27 Clearing Storage Registers 29 Storage Register Arithmetic 29 Section 2 Percentage and Calendar Func...

Page 6: ...ations 49 Specifying the Number of Compounding Periods and the Periodic Interest Rate 49 Calculating the Number of Payments or Compounding Periods 49 Calculating the Periodic and Annual Interest Rates 55 Calculating the Present Value 56 Calculating the Payment Amount 59 Calculating the Future Value 61 Odd Period Calculations 63 Amortization 69 Section 4 Additional Financial Functions 72 Discounted...

Page 7: ...ons 100 One Number Functions 100 The Power Function in RPN Mode 102 The Power Function in ALG Mode 102 Part II Programming 105 Section 8 Programming Basics 106 Why Use Programs 106 Creating a Program 106 Running a Program 108 Program Memory 1 10 Identifying Instructions in Program Lines 1 10 Displaying Program Lines 1 1 1 The 000 Instruction and Program Line 000 1 14 Expanding Program Memory 1 14 ...

Page 8: ...Fees 158 Price of a Mortgage Traded at a Discount or Premium 161 Yield of a Mortgage Traded at a Discount or Premium 163 The Rent or Buy Decision 165 Deferred Annuities 171 Section 13 Investment Analysis 174 Partial Year Depreciation 174 Straight Line Depreciation 174 Declining Balance Depreciation 179 Sum of the Years Digits Depreciation 183 Full and Partial Year Depreciation with Crossover 187 E...

Page 9: ... Number Functions and the Stack 235 Mathematics Functions 236 Percentage Functions 236 Calendar and Financial Functions 237 The LAST X Register and the Key 238 Chain Calculations in RPN Mode 239 Arithmetic Calculations with Constants 240 Appendix B Algebraic Mode ALG 242 Simple Arithmetic Calculations in ALG Mode 242 Keying in Negative Numbers 243 Chain Calculations in ALG Mode 243 The Key in ALG ...

Page 10: ...turn 257 Calendar 257 Actual Day Basis 257 30 360 Day Basis 257 Bonds 258 Black Scholes Formula for Valuing European Options 259 Depreciation 259 Straight Line Depreciation 260 Sum of the Years Digits Depreciation 260 Declining Balance Depreciation 260 Modified Internal Rate of Return 261 Advance Payments 261 Interest Rate Conversions 261 Finite Compounding 261 Continuous Compounding 261 Statistic...

Page 11: ...Limited Hardware Warranty and Customer Care 268 Customer Care 269 Regulatory Information 272 Disposal of Waste Equipment by Users in Private Household in the European Union 274 Appendix G United Kingdom Calculations 275 Mortgages 275 Annual Percentage Rate APR Calculations 276 Bond Calculations 276 Function Key Index 278 Programming Key Index 282 Subject Index 284 ...

Page 12: ...erest compounded monthly This is an example of a compound interest calculation All such problems involve at least three of the following quantities z n the number of compounding periods z i the interest rate per compounding period z PV the present value of a compounded amount z PMT the periodic payment amount z FV the future value of a compounded amount In this particular example z n is 4 years 12...

Page 13: ...s the number of compounding periods 6gC 0 50 Calculates and stores the periodic interest rate 500P 500 00 Stores periodic payment amount g 500 00 Sets payment mode to Begin 21 396 61 Amount required to be deposited Example 2 We now need to determine how to accumulate the required deposit by the time your daughter enters college 14 years from now Let s say that she has a paid up 5 000 insurance pol...

Page 14: ...6gC 0 50 Calculates and stores the periodic interest rate 11024 82M 11 024 82 Stores the future value required g 11 024 82 Sets payment mode to End P 42 03 Monthly payment required Example 4 Suppose you cannot find a bank that currently offers an account with 6 annual interest compounded monthly but you can afford to make 45 monthly payments What is the minimum interest rate that will enable you ...

Page 15: ...Part I Problem Solving ...

Page 16: ... Many keys on the hp 12c platinum perform two or even three functions The primary function of a key is indicated by the characters printed in white on the upper face of the key The alternate function s of a key are indicated by the characters printed in gold above the key and the characters printed in blue on the lower face of the key These alternate functions are specified by pressing the appropr...

Page 17: ...the digit keys in sequence just as if you were writing the number on paper A decimal point must be keyed in using the decimal point key if it is part of the number unless it appears to the right of the last digit Digit Separators As a number is keyed in each group of three digits to the left of the decimal point is automatically separated in the display When the calculator is first turned on after...

Page 18: ...ositive if you moved the decimal point to the right this would occur for numbers less than one the exponent is negative To key the number into the display simply key in the mantissa press Æ enter exponent then key in the exponent If the exponent is negative press Þ after pressing Æ For example to key in 1 781 400 000 000 we move the decimal point 12 places to the left giving a mantissa of 1 7814 a...

Page 19: ...Program memory only when pressed in Program mode fCLEARG Financial registers fCLEARH Data storage registers financial registers stack and LAST X registers and display Note In ALG mode it is a good idea to begin calculations by pressing OO This will ensure that there are no pending arithmetic calculations that might interfere with the solution of a new problem The reason this key is pressed twice i...

Page 20: ...raditional way using parentheses if needed To select RPN mode Press f to set the calculator to RPN mode When the calculator is in RPN mode the RPN status indicator is lit To select ALG mode Press f to set the calculator to ALG mode When the calculator is in ALG mode the ALG status indicator is lit Example Suppose you want to calculate 1 2 3 In RPN mode you enter the first number press the key ente...

Page 21: ...d number from the first 3 Key in the second number 4 Press or z to perform the desired operation For example to calculate 13 2 proceed as follows Keystrokes RPN mode Display 13 13 Keys the first number into the calculator 13 00 Pressing separates the second number from the first 2 2 Keys the second number into the calculator z 6 50 Pressing the operation key calculates the answer Notice that after...

Page 22: ...e first number and prepares to add the second 23 8 23 8 Keys the second number 44 90 completes the calculation Once a calculation has been completed z pressing another digit key starts a new calculation or z pressing an operator key continues the calculation Keystrokes ALG mode Display OO 0 00 Clears any pending operations 77 35 77 35 90 89 13 54 completes the calculation 65gr 12 96 75 New calcula...

Page 23: ... then not later so that you see the results of all intermediate calculations as well as the bottom line Example Suppose you ve written three checks without updating your checkbook and you ve just deposited your paycheck for 1 053 into your checking account If your latest balance was 58 33 and the checks were written for 22 95 13 70 and 10 14 what is the new balance Solution When written down on pa...

Page 24: ...w current balance appears in the display The preceding example demonstrates how the hp 12c platinum calculates just as you would using pencil and paper except a lot faster Let s see this happening in a different type of calculation one that involves multiplying groups of two numbers and then adding the results This is the type of calculation that would be required to total up an invoice consisting...

Page 25: ...calculates with them at the proper time just as you would yourself But with the hp 12c platinum you don t need to write down the results of an intermediate calculation and you don t even need to manually store it and recall it later By the way notice that in step 2 you needed to press again This is simply because you were again keying in two numbers immediately following each other without perform...

Page 26: ...des 381 by 18 5 68z 1 400 43 Multiplies by 68 1 9 737 07 Divides by 1 9 and displays the result Parentheses Calculations In ALG mode parentheses can be used in calculations to change the order in which operations are evaluated When there are pending open parentheses the status indicator will be shown in the display As open parentheses are closed the expression contained within the parentheses is e...

Page 27: ...rs are stored automatically up to 20 data storage registers are available for manual storage of numbers These data storage registers are designated R0 through R9 and R 0 through R 9 Still other storage registers referred to as the financial registers are reserved for numbers used in financial calculations Storing and Recalling Numbers To store the number from the display into a data storage regist...

Page 28: ...st of the computer in R0 500 2 500 00 Stores the cost of the printer in R2 Turns the calculator off Later that same day Keystrokes RPN mode Display 500 00 Turns the calculator back on 0 1 250 00 Recalls the cost of the computer to the display 6 7 500 00 Multiplies the quantity ordered to get the cost of the computers 2 500 00 Recalls the cost of the printer to the display 8 000 00 Total invoice Ke...

Page 29: ...torage register then store the result back into the same register without altering the number in the display The hp 12c platinum enables you to do all this in a single operation 1 Press 2 Press or z to specify the desired operation 3 Key in the register number When storage register arithmetic is performed the new number in the register is determined according to the following rule Storage register...

Page 30: ...from the balance in R0 Note that the display continues to show the amount subtracted the answer is placed only in R0 13 7 0 13 70 Subtracts the second check 10 14 0 10 14 Subtracts the third check 1053 0 1 053 00 Adds the deposit 0 1 064 54 Recalls the number in R0 to check the new balance ...

Page 31: ...de to find the amount corresponding to a percentage of a number 1 Key in the base number 2 Press 3 Key in the percentage 4 Press b For example to find 14 of 300 Keystrokes RPN mode Display 300 300 Keys in the base number 300 00 Pressing separates the next number entered from the first number just as when an ordinary arithmetic calculation is performed 14 14 Keys in the percentage b 42 00 Calculate...

Page 32: ...the base number 300 00 Tells the calculator to multiply the 300 by the percentage entered next 14 14 Keys in the percentage b 0 14 Divides the percentage by 100 42 00 Calculates the amount In most cases b divides a number by 100 The one exception is when a plus or minus sign precedes the number For instance 25 b results in 0 25 To find 25 of 200 press 200 25 b Result is 50 Note This is the last ti...

Page 33: ... 00 Amount of discount 21 390 00 Base amount less discount 6b 1 283 40 Amount of tax on 21 390 22 673 40 Total cost base amount less discount plus tax Net Amount in ALG Mode In ALG mode you can calculate a net amount all in one calculation For example to decrease 200 by 25 just enter 200 25b Result is 150 Example You borrow 1 250 from a relative and agree to repay the loan in a year with 7 simple ...

Page 34: ...es an increase while a negative answer indicates a decrease If you are calculating a percent difference over time the base number is typically the amount occurring first Example Yesterday your stock fell from 58 50 to 53 25 per share What is the percent change Note that the key is the same as the key in ALG mode Keystrokes Display 58 5 58 50 Keys in the base number and separates it from the other ...

Page 35: ...parates it from the second 2 36 6 28 Adds the second number 1 67 7 95 Adds the third number to get the total 2 36 2 36 Keys in 2 36 to find what percentage it is of the number in the display Z 29 69 Europe had nearly 30 of the total sales In RPN mode the hp 12c platinum holds the total amount inside after a percent of total is calculated Therefore to calculate what percentage another amount is of ...

Page 36: ... in the display Z 29 69 Europe had nearly 30 of the total sales Percent of Total in ALG Mode In ALG mode to calculate what percentage one number is of another 1 Calculate the total amount by adding the individual amounts just as in a chain arithmetic calculation 2 Key in the number whose percentage equivalent you wish to find 3 Press Z Example Last month your company posted sales of 3 92 million i...

Page 37: ...to find what percentage it is of the number in the display Z 29 69 Europe had nearly 30 of the total sales Calendar Functions The calendar functions provided by the hp 12c platinum gD and gÒ can handle dates from October 15 1582 through November 25 4046 These calendar functions work the same in both RPN and ALG modes Date Format For each of the calendar functions and also for bond calculations fE ...

Page 38: ...ime the calculator is turned on However if Continuous Memory is reset the date format is set to month day year Future or Past Dates To determine the date and day that is a given number of days from a given date 1 Key in the given date and press 2 Key in the number of days 3 If the other date is in the past press Þ 4 Press gD The answer calculated by the gD function is displayed in a special format...

Page 39: ...lay shown assumes date remains from preceding example The full date is not now displayed because the display format is set to show only two decimal places as described in Section 5 14 052004 14 05 Keys in the date and separates it from the number of days to be entered 120gD 11 09 2004 6 The expiration date is 11 September 2004 a Saturday When gD is executed as an instruction in a running program t...

Page 40: ...again will return the original answer to the display Example Simple interest calculations can be done using either the actual number of days or the number of days counted on the basis of a 30 day month What would be the number of days counted each way to be used in calculating the simple interest accruing from June 3 2004 to October 14 2005 Assume that you normally express dates in the month day y...

Page 41: ...al Registers To display a number stored in a financial register press followed by the corresponding key Which operation is performed when one of these keys is pressed depends upon the last preceding operation performed If a number was just stored into a financial register using n P M gA or gC pressing one of these five keys calculates the corresponding value and stores it into the corresponding re...

Page 42: ... as described below Furthermore with the accrued interest in the display you can calculate the total amount principal plus accrued interest by pressing in RPN mode or in ALG mode 1 Key in or calculate the number of days then press n 2 Key in the annual interest rate then press 3 Key in the principal amount then press Þ 4 Press fÏ to calculate and display the interest accrued on a 360 day basis 5 I...

Page 43: ...lace the last step with the step below Keystrokes ALG mode Display 455 25 Total amount principal plus accrued interest Example 2 Your friend agrees to the 7 interest on the loan from the preceding example but asks that you compute it on a 365 day basis rather than a 360 day basis What is the amount of accrued interest he will owe you in 60 days and what is the total amount owed Keystrokes RPN mode...

Page 44: ...our calculator in a financial calculation is the cash flow diagram This is simply a pictorial representation of the timing and direction of financial transactions labeled in terms that correspond to keys on the calculator The diagram begins with a horizontal line called a time line It represents the duration of a financial problem and is divided into compounding periods For example a financial pro...

Page 45: ...h 67 If n is a noninteger that is there is at least one nonzero digit to the right of the decimal point calculations of i PV PMT and FV are performed in Odd Period mode z i is the interest rate per compounding period The interest rate shown in the cash flow diagram and entered into the calculator is determined by dividing the annual interest rate by the number of compounding periods In the problem...

Page 46: ... calculator with the proper sign plus or minus in accordance with The Cash Flow Sign Convention Money received arrow pointing up is entered or displayed as a positive value Money paid out arrow pointing down is entered or displayed as a negative value The Payment Mode One more bit of information must be specified before you can solve a problem involving periodic payments Such payments can be made ...

Page 47: ...pear under Compound Interest Calculations later in this section If your particular problem does not match any of those shown you can solve it nevertheless by first drawing a cash flow diagram then keying the quantities identified in the diagram into the corresponding registers Remember always to observe the sign convention when keying in PV PMT and FV The terminology used for describing financial ...

Page 48: ...48 Section 3 Basic Financial Functions ...

Page 49: ...into n The same is true for i Values of n and i are calculated and stored like this in Example 2 on page 60 If interest is compounded monthly you can use a shortcut provided on the calculator to calculate and store n and i z To calculate and store n key the number of years into the display then press gA z To calculate and store i key the annual rate into the display then press gC Note that these k...

Page 50: ... value of the final payment with which you can calculate a balloon payment or desire to know the payment value for n equal payments you will need to press one of the other financial keys as shown in the following two examples Example 1 You re planning to build a log cabin on your vacation property Your rich uncle offers you a 35 000 loan at 10 5 interest If you make 325 payments at the end of each...

Page 51: ...al number of payments M 181 89 Calculates FV which equals the overpayment if 328 full payments were made P 325 00 Recalls payment amount 143 11 Final fractional payment Keystrokes ALG mode Display 328n 328 00 Stores total number of payments M 181 89 Calculates FV which equals the overpayment if 328 full payments were made You could skip this step since 328 is already stored in the n register If yo...

Page 52: ...ows Keystrokes RPN mode Display 327n 327 00 Stores number of full payments M 141 87 Calculates FV which is the balance remaining after 327 full payments P 325 00 Recalls payment amount 466 87 Final balloon payment Keystrokes ALG mode Display 327n 327 00 Stores number of full payments M 141 87 Calculates FV which is the balance remaining after 327 full payments P 325 00 Recalls payment amount 466 8...

Page 53: ...N mode Display fCLEARG 6 25 24z 0 26 Calculates and stores i 775Þ 775 00 Stores PV with minus sign for cash paid out 50ÞP 50 00 Stores PMT with minus sign for cash paid out 4000M 4 000 00 Stores FV g 4 000 00 Sets the payment mode to End n 58 00 Number of semimonthly deposits 2z 29 00 Number of months Keystrokes ALG mode Display fCLEARG 6 25z24 0 26 Calculates and stores i 775Þ 775 00 Stores PV w...

Page 54: ...000 Keystrokes ALG mode Display MM 4 027 27 Calculates FV which equals the balance in the account if 58 full deposits were made P 50 00 Recalls amount of deposits 3 977 27 Calculates the balance in the account if 57 full deposits were made and interest accrued during the 58th month In this example M must be pressed twice since the preceding key pressed was z in RPN mode and in ALG mode If we had s...

Page 55: ... the cash flow sign convention 4 If a PMT was entered press g or g to set the payment mode 5 Press to calculate the periodic interest rate 6 To calculate the annual interest rate in RPN mode key in the number of periods per year then press To calculate the annual interest rate in ALG mode press key in the number of periods per year then press Example What annual interest rate must be obtained to ...

Page 56: ... 1 61 Periodic quarterly interest rate 4 6 44 Annual interest rate Calculating the Present Value 1 Press fCLEARG to clear the financial registers 2 Enter the number of payments or periods using n or gA 3 Enter the periodic interest rate using or gC 4 Enter either or both of the following z Payment amount using P z Future value using M Note Remember to observe the cash flow sign convention 5 If a P...

Page 57: ...ay for the car Assume the purchase date is one month prior to the date of the first payment Keystrokes RPN mode Display fCLEARG 4gA 48 00 Calculates and stores n 5 9gC 0 49 Calculates and stores i 450ÞP 450 00 Stores PMT with minus sign for cash paid out g 450 00 Sets payment mode to End 19 198 60 Maximum amount of loan 1500 20 698 60 Maximum purchase price In ALG mode press the keys listed for R...

Page 58: ... amount the company can pay for the condominiums in order to realize at least a 12 annual yield Keystrokes Display fCLEARG 5n 5 00 Stores n 12 12 00 Stores i 17500P 17 500 00 Stores PMT Unlike in the previous problem here PMT is positive since it represents cash received 540000M 540 000 00 Stores FV g 540 000 00 Sets payment mode to End 369 494 09 The maximum purchase price to provide a 12 annual...

Page 59: ...re value using M Note Remember to observe the cash flow sign convention 5 Press g or g to set the payment mode 6 Press P to calculate the payment amount Example 1 Calculate the payment amount on a 29 year 243 400 mortgage at 5 25 annual interest compounded monthly Keystrokes Display fCLEARG 29gA 348 00 Calculates and stores n 5 25gC 0 44 Calculates and stores i 243400 243 400 00 Stores PV g 243 ...

Page 60: ...ate how much these deposits should be Keystrokes RPN mode Display fCLEARG 15 2µw 30 00 Calculates and stores n 9 75 2z 4 88 Calculates and stores i 3200Þ 3 200 00 Stores PV with minus sign for cash paid out 60000M 60 000 00 Stores FV g 60 000 00 Sets payment mode to End P 717 44 Semiannual payment with minus sign for cash paid out Keystrokes ALG mode Display fCLEARG 15µ2w 30 00 Calculates and sto...

Page 61: ...e Remember to observe the cash flow sign convention 5 If a PMT was entered press g or g to set the payment mode 6 Press M to calculate the future value Example 1 In Example 1 on page 59 we calculated that the payment amount on a 29 year 243 400 mortgage at 5 25 annual interest compounded monthly is 1 363 29 If the seller requests a balloon payment at the end of 5 years what would be the amount of...

Page 62: ...at the beginning of each month into a new account that pays 6 25 annual interest compounded monthly how much will you have in the account after 2 years Keystrokes Display fCLEARG 2gA 24 00 Calculates and stores n 6 25gC 0 52 Calculates and stores i 50ÞP 50 00 Stores PMT with minus sign for cash paid out g 50 00 Sets payment mode to Begin M 1 281 34 Balance after 2 years ...

Page 63: ...gular payment period However interest often begins to accrue prior to the beginning of the first regular payment period The period from the date interest begins accruing to the date of the first payment being not equal to the regular payment periods is sometimes referred to as an odd first period For simplicity in using the hp 12c platinum we will always regard the first period as equal to the rem...

Page 64: ...therefore cannot be greater than one full period Calculations of i PMT and FV are performed using the present value at the end of the odd period This is equal to the number in the PV register plus the interest accrued during the odd period When calculating PV in Odd Period mode the calculator returns a value equal to the present value at the beginning of the odd period and stores it in the PV regi...

Page 65: ...nd calculations will then be performed using simple interest for the odd period Example 1 A 36 month loan for 4 500 accrues interest at a 5 annual percentage rate APR with the payments made at the end of each month If interest begins accruing on this loan on February 15 2004 so that the first period begins on March 1 2004 calculate the monthly payment with the odd days counted on the basis of a 30...

Page 66: ...mode Display Æ Turns on the C indicator in the display so that compound interest will be used for the odd period 2 152004 2 15 Keys in the date interest begins accruing and separates it from the next date entered 3 012004 3 012004 Keys in the date of the beginning of the first period gÒ 15 00 Actual number of odd days 16 00 Number of odd days counted on the basis of a 30 day month z30 0 53 Divides...

Page 67: ... and separates it from the next date entered 8 012004 8 012004 Keys in the date of the beginning of the first period gÒ 13 00 Actual number of odd days 30z 0 43 Divides by the length of a monthly period to get the fractional part of n 42 n 42 43 Adds the fractional part of n to the number of complete payment periods then stores the result in n 3950 3 950 00 Stores PV 120ÞP 120 00 Stores PMT with m...

Page 68: ...result in n 3950 3 950 00 Stores PV 120ÞP 120 00 Stores PMT with minus sign for cash paid out 1 16 Periodic monthly interest rate 12 13 95 Annual percentage rate APR Before leaving this Odd Period mode example you may now press Æ to turn the C annunciator off if needed Note that when the calculator is not in Odd Period mode the status of the C annunciator actually has no effect on calculator opera...

Page 69: ...yments just amortized press dd 10 To display the remaining balance of the loan press 11 To display the total number of payments amortized press n Example For a house you re about to buy you can obtain a 25 year mortgage for 250 000 at 5 25 annual interest This requires payments of 1 498 12 at the end of each month Find the amounts that would be applied to interest and to the principal from the fir...

Page 70: ...2f 12 739 18 Portion of second year s payments applied to interest 5 238 26 Portion of second year s payments applied to principal dd 12 00 Number of payments just amortized 239 790 83 Balance remaining after 2 years n 24 00 Total number of payments amortized Pressing or n displays the number in the PV or n register When you did so after each of the last two calculations you may have noticed that ...

Page 71: ...ted on page 69 beginning with step 6 Example Suppose you obtained a 30 year mortgage instead of a 25 year mortgage for the same principal 250 000 and at the same interest rate 5 25 as in the preceding example Calculate the monthly payment then calculate the amounts applied to interest and to the principal from the first month s payment Since the interest rate is not being changed do not press fCLE...

Page 72: ...st year and so on up to the final cash flow CF6 at the end of the sixth year In the following diagram the initial investment is denoted by CF0 and is depicted as an arrow pointing down from the time line since it is cash paid out Cash flows CF1 and CF4 also point down from the time line because they represent projected cash flow losses NPV is calculated by adding the initial investment represented...

Page 73: ...lows If there are no equal consecutive cash flows use the procedure described and then summarized below With this procedure NPV and IRR problems involving up to 80 cash flows in addition to the initial investment CF0 can be solved If two or more consecutive cash flows are equal for example if the cash flows in periods three and four are both 8 500 you can solve problems involving more than 80 cash...

Page 74: ...r the interest rate using or gC 2 Press fl The calculated value of NPV appears in the display and also is automatically stored in the PV register Example An investor has an opportunity to buy a duplex for 80 000 and would like a return of at least 13 He expects to keep the duplex 5 years and then sell it for 130 000 and he anticipates the cash flows shown in the diagram below Calculate NPV to dete...

Page 75: ... to 99 each amount occurs consecutively This number is designated Nj corresponding to cash flow amount CFj and is entered using the ga keys Each Nj is stored in a special register inside the calculator This method can of course be used for problems involving fewer than 80 cash flows and it will require fewer storage registers than the method described above under Calculating NPV for Ungrouped Cash...

Page 76: ...of times that cash flow amount occurs consecutively then press ga If ga is not pressed the calculator assumes that Nj is 1 for the CFj just entered 6 Repeat steps 4 and 5 for each CFj and Nj until all cash flows have been entered With the amounts of the cash flows and the number of times they occur consecutively stored in the calculator NPV can be calculated by entering the interest rate and press...

Page 77: ...flow amount 3ga 3 00 Number of times this cash flow amount occurs consecutively 9100gK 9 100 00 Next cash flow amount 9000gK 9 000 00 Next cash flow amount 2ga 2 00 Number of times this cash flow amount occurs consecutively 4500gK 4 500 00 Next cash flow amount 100000gK 100 000 00 Final cash flow amount n 7 00 Seven different cash flow amounts have been entered 13 5 13 50 Stores i fl 907 77 NPV Si...

Page 78: ...r of periods per year As noted above the calculator may take several seconds or even minutes to produce an answer for IRR This is because the mathematical calculations for finding IRR are extremely complex involving a series of iterations that is a series of successive calculations In each iteration the calculator uses an estimate of IRR as the interest rate in a computation of NPV The iterations ...

Page 79: ...y that is to review each CFj and Nj pair press ga gK repeatedly This displays Nj followed by CFj beginning with the final cash flow amount and proceeding to N0 and CF0 Note Neither fL nor fl changes the number in the n register However each time gK is pressed the number in the n register is decreased by 1 If this is done or if you manually change the number in the n register in order to display a ...

Page 80: ...he number in the n register to its original value Changing Cash Flow Entries z To change a cash flow amount 1 Key the amount into the display 2 Press 3 Key in the number of the register containing the cash flow amount to be changed z To change the number of times a cash flow amount occurs consecutively that is to change the Nj for a CFj 1 Store the number of that cash flow amount that is j in the ...

Page 81: ...V for a 13 5 return Keystrokes Display 9000 2 9 000 00 Stores the new CF2 in R2 13 5 13 50 Stores i fl 644 75 The new NPV Since this NPV is negative the investment would decrease the financial value of the investor s assets Example 2 Change N5 from 2 to 4 then calculate the new NPV Keystrokes Display 5n 5 00 Stores j in the n register 4ga 4 00 Stores the new N5 7n 7 00 Resets the number in the n r...

Page 82: ...hen press 4 Key in the maturity redemption date 5 Press fE The price is shown in the display and also is stored in the PV register The interest accrued since the last interest date is held inside the calculator to display the interest press to add the interest to the price press in RPN mode and in ALG mode Example What price should you pay on April 28 2004 for a 6 75 U S Treasury bond that matures...

Page 83: ...er that the fS function may take a significant amount of time to produce an answer during which the calculator displays running Example The market is quoting 122 125 for the bond described in the preceding example What yield will that provide Keystrokes Display 122 125 122 13 Enters quoted price 6 75P 6 75 Enters coupon rate 4 282004 4 28 Enters settlement purchase date 6 042018 6 042018 Enters ma...

Page 84: ...ress z fV for depreciation using the straight line method z fÝfor depreciation using the sum of the years digits method z f for depreciation using the declining balance method fV fÝ and f each place the amount of depreciation in the display To display the remaining depreciable value the book value less the salvage value after the depreciation has been calculated press Example A metalworking machin...

Page 85: ...year To calculate depreciation and the remaining depreciable value when the acquisition date of the asset does not coincide with the beginning of the fiscal accounting year refer to the procedures in Section 13 That section also includes a procedure for depreciation calculations when changing from the declining balance method to the straight line method and a procedure for calculating excess depre...

Page 86: ...r is interrupted You can also manually reset Continuous Memory as follows 1 Turn the calculator off 2 Hold down the key and press When Continuous Memory is reset z All registers are cleared z Program memory consists of eight program lines each containing the instruction g 000 z Display format is set to the standard format with two decimal places z Date format is set to month day year z Payment mod...

Page 87: ...hrough 4 the second digit is not affected Rounding occurs regardless of how many decimal places are displayed Several options are provided for controlling how numbers appear in the display But regardless of which display format or how many displayed decimal places you specify the number inside the calculator which appears altered in the display is not altered unless you use the B V Ý or functions ...

Page 88: ...display format for all numbers that can be displayed in that format Scientific Notation Display Format In scientific notation a number is displayed with its mantissa at the left and a two digit exponent at the right The mantissa is simply the first seven digits in the number and has a single nonzero digit to the left of the decimal point The exponent is simply how many decimal places you would mov...

Page 89: ... press fCLEARX and hold down the X key The display will show all 10 digits of the number as long as you hold down the X key after you release the key the number will again be displayed in the current display format For instance if the display still contains the result from the preceding example Keystrokes Display fCLEARX 1487456320 All 10 digits of the number inside the calculator 1 487456 01 Disp...

Page 90: ... so that you have unfortunately keyed in the second number first To correct this mistake merely exchange the first and second numbers by pressing the exchange key Keystrokes RPN mode Display 25 83 144 25 144 25 Oops You mistakenly keyed in the second number first 25 83 Exchanges the first and second numbers The first number keyed in is now in the display 118 42 The answer is obtained by pressing t...

Page 91: ...ost into display again 1 095 00 Cost of a package of 250 Another method for doing arithmetic calculations with constants is described on page 240 Recovering From Errors in Digit Entry Example Suppose you want to divide the total annual production for one of your firm s products 429 000 by the number of retail outlets 987 in order to calculate the average number distributed by each outlet Unfortuna...

Page 92: ...92 Section 5 Additional Operating Features Keystrokes RPN mode Display 987z 434 65 The correct answer ...

Page 93: ...enter each data point referred to as an x value key the x value into the display then press _ In two variable statistical calculations to enter each data pair referred to as the x and y values 1 Key the y value into the display 2 Press 3 Key the x value into the display 4 Press _ Each time you press _ the calculator does the following z The number in R1 is increased by 1 and the result is copied i...

Page 94: ...istics can easily be corrected Simply key in the incorrect data point or data pair again as if it were new but press g instead of _ Then enter the correct data point or data pair and press _ Mean Pressing gÖ calculates the means arithmetic averages of the x values x and of the y values y The mean of the x values appears in the display after gÖ is pressed to display the mean of the y values press E...

Page 95: ...s sample Keystrokes Display fCLEAR 0 00 Clears statistics registers 32 17000_ 32 00 1 00 First entry 40 25000_ 40 00 2 00 Second entry 45 26000_ 45 00 3 00 Third entry 40 20000_ 40 00 4 00 Fourth entry 38 21000_ 38 00 5 00 Fifth entry 50 28000_ 50 00 6 00 Sixth entry 35 15000_ 35 00 7 00 Total number of entries in the sample gÖ 21 714 29 Mean dollar sales per month x 40 00 Mean workweek in hours y...

Page 96: ... standard deviation based on a sample of the population Thus current statistical convention calls them sample standard deviations So we have assumed that the seven salespersons are a sample of the population of all salespersons and our formulas derive best estimates of the population from the sample What if the seven salespersons constituted the whole population of salespersons Then we wouldn t ne...

Page 97: ...o variable statistical data accumulated in the statistics registers you can estimate a new y value y given a new x value and estimate a new x value x given a new y value To calculate y and Q 1 Key in a new x value 2 Press gR To calculate x 1 Key in a new y value 2 Press gQ Example Using the accumulated statistics from the preceding problem estimate the amount of sales delivered by a new salesperso...

Page 98: ... B in RPN mode press 1gR d To compute the slope of the line B in ALG mode press these keys 1gR d Example Compute the slope and intercept of the regression line in the preceding example Keystrokes RPN mode Display 0gR 15 55 y intercept A projected value for x 0 1 gR d 0 001 Slope of the line B indicates the change in the projected values caused by an incremental change in the x value Keystrokes ALG...

Page 99: ...allon 7 gallons at 1 24 per gallon 10 gallons at 1 20 per gallon and 17 gallons at 1 18 per gallon You want to find the average cost per gallon of gasoline purchased If you purchased the same quantity at each station you could determine the simple arithmetic average or mean using the gÖ keys But since you know the value of the item gasoline and its corresponding weight number of gallons purchased ...

Page 100: ...is the logarithm to the base e of the number in the display To calculate the common logarithm that is the logarithm to the base 10 of the number in the display calculate the natural logarithm then press 10g z in RPN mode and z10g in ALG mode Exponential Pressing g calculates the exponential of the number in the display that is it raises the base e to the number in the display Factorial Pressing ge...

Page 101: ...le to find the reciprocal of 0 258 Keystrokes Display 258 0 258 Keys the number into the display y 3 88 The reciprocal of 0 258 the original number Any of the above functions can be done with a number in the display resulting from a previous calculation as well as with a number you have just keyed in The examples below indicate how gF can recall the original number for further use in RPN mode Keys...

Page 102: ...nent from the first the base 3 Key in the exponent which is designated by the x on the key 4 Press q to calculate the power To Calculate Keystrokes RPN mode Display 21 4 2 1 4q 2 64 2 1 4 2 1 4Þq 0 38 2 3 2Þ 3q 8 00 3 2 or 21 3 2 3yq 1 26 The Power Function in ALG Mode To calculate a power of a number that is yx in ALG mode do the following 1 Key in the base number which is designated by the y on ...

Page 103: ...Section 7 Mathematics and Number Alteration Functions 103 To Calculate Keystrokes ALG mode Display 3 2 or 21 3 2q3y 1 26 ...

Page 104: ......

Page 105: ...Part II Programming ...

Page 106: ... created and saved in RPN mode should only be executed in RPN mode and programs or steps created and saved in ALG mode should only be executed in ALG mode You can also create steps in your program to switch to the appropriate mode 3 Press fs to set the calculator to Program mode When the calculator is in Program mode functions are not executed when they are keyed in but instead are stored inside t...

Page 107: ...e less discount plus handling charge Keystrokes ALG mode Display 200 200 Keys in cost of item 200 00 Separates cost of item from percentage to be keyed in next 25b 50 00 Amount of discount 150 00 Price less discount 5 5 Handling charge 155 00 Net cost price less discount plus handling charge Next set the calculator to Program mode and erase any program s already stored Keystrokes Display fs Sets c...

Page 108: ...times called execute a program 1 Press fs to set the calculator back to Run mode If the calculator is already in Run mode that is the PRGM status indicator in the display is not lit skip this step 2 Key any required data into the calculator just as if you were calculating manually When a program is run it uses the data already keyed into the display and the registers inside the calculator 3 Press ...

Page 109: ...calculated f 155 00 Sets ALG mode 625 625 Keys in price of typewriter t 473 75 Net cost of typewriter 159 159 Keys in list price of chair t 124 25 Net cost of chair That s all there is to creating and running simple programs But if you want to use programs frequently you ll want to know more about programming such as how to check what keystrokes are stored in program memory how many keystrokes can...

Page 110: ... instruction has been stored in that program line No code is shown for program line 000 since no regular instruction is stored there Identifying Instructions in Program Lines Each key on the hp 12c platinum keyboard except for the digit keys 0 through 9 is identified by a two digit keycode that corresponds to the key s position on the keyboard The first digit in the keycode is the number of the ke...

Page 111: ...lculator is currently set Occasionally you ll want to check several or all of the instructions stored in program memory The hp 12c platinum enables you to review program instructions either forward or backward through program memory z Pressing Ê single step while the calculator is in Program mode advances the calculator to the next line in program memory then displays that line number and the keyc...

Page 112: ...ays current line of program memory Ê 001 36 Program line 001 Ê 002 2 Program line 002 digit 2 Keystrokes ALG mode Display fs 000 Sets calculator to Program mode and displays current line of program memory Ê 001 30 Program line 001 Ê 002 2 Program line 002 digit 2 Pressing gÜ does the reverse Keystrokes RPN mode Display gÜ 001 36 Program line 001 gÜ 000 Program line 000 Keystrokes ALG mode Display ...

Page 113: ...m line 001 Release Ê 007 40 Program line 007 Keystrokes ALG mode Display Ê 001 30 Program line 001 Release Ê 007 36 Program line 007 Program line 007 contains the last instruction you keyed into program memory However if you press Ê again you ll see that this is not the last line stored in program memory Keystrokes Display Ê 008 43 33 000 Program line 008 As you should now be able to tell from the...

Page 114: ... in line 008 in fact in all program lines before you keyed in the program If no instructions have been keyed into program memory if Continuous Memory is reset or if fCLEARÎ is pressed in Program mode the instruction i000 is automatically stored in program lines 001 through 008 As you key each instruction into program memory it replaces the i000 instruction in that program line If your program shou...

Page 115: ...mize program length is to replace numbers consisting of more than just one digit like the number 25 in lines 002 and 003 of the program keyed in above by a instruction and then storing the number in the designated storage register before running the program In this case this would save one program line since the instruction requires only one program line not two as are required by the number 25 Of...

Page 116: ...e assuming the calculator is still in Program mode you can set it to program line 000 as follows Keystrokes Display gi 000 000 Program line 000 Executing a Program One Line at a Time Pressing Ç repeatedly with the calculator in Program mode as described earlier enables you to verify that the program you have stored is identical to the program you wrote that is to verify that you have keyed the ins...

Page 117: ...t of executing program line 001 Ç 002 2 Program line 002 2 2 Result of executing program line 002 Ç 003 5 Program line 003 5 25 Result of executing program line 003 Ç 004 25 Program line 004 b 156 25 Result of executing program line 004 Ç 005 30 Program line 005 468 75 Result of executing program line 005 Ç 006 5 Program line 006 5 5 Result of executing program line 006 Ç 007 40 Program line 007 4...

Page 118: ...04 b 156 25 Result of executing program line 004 Ç 005 40 Program line 005 468 75 Result of executing program line 005 Ç 006 5 Program line 006 5 5 Result of executing program line 006 Ç 007 36 Program line 007 473 75 Result of executing program line 007 the last line of the program Pressing gÜ while the calculator is in Run mode sets the calculator to the previous line in program memory then disp...

Page 119: ...nd TOTAL columns for each item on the jewelry distributor s invoice shown on the next page and also calculates the total in each of these columns for all items on the invoice Assume the sales tax is 6 75 To conserve lines of program memory instead of keying in the tax rate before the b instruction we ll store it in register R0 and recall it before the b instruction Before storing the program in pr...

Page 120: ... but we ll include gu instructions in the program so that the intermediate results AMOUNT and TAX are automatically displayed when the program is executed Keystrokes RPN mode Display 6 75 0 6 75 Stores tax rate in R0 fCLEAR 0 00 Clears the registers in R1 through R6 13 13 Keys in quantity of item 13 00 Separates quantity of item from cost of item to be keyed in next 68 5 68 5 Keys in cost of item ...

Page 121: ...trokes ALG mode Display 6 75 0 6 75 Stores tax rate in R0 fCLEAR 0 00 Clears the registers in R1 through R6 13 13 Keys in quantity of item 13 00 Separates quantity of item from cost of item to be keyed in next 68 5 68 5 Keys in cost of item 890 50 AMOUNT 1 890 50 Adds AMOUNT to sum of AMOUNT entries in register R1 890 50 Prepares to add tax 0 6 75 Recalls tax rate to display b 60 11 TAX 2 60 11 Ad...

Page 122: ...mode fCLEARÎ 000 Clears program memory 001 20 gu 002 43 31 Pauses to display AMOUNT 1 003 44 40 1 0 004 45 0 b 005 25 gu 006 43 31 Pauses to display TAX 2 007 44 40 2 008 40 3 009 44 40 3 Keystrokes ALG mode Display fs Sets calculator to Program mode fCLEARÎ 000 Clears program memory 001 20 002 34 003 36 gu 004 43 31 Pauses to display AMOUNT 1 005 44 40 1 006 40 0 007 45 0 b 008 25 gu 009 43 31 Pa...

Page 123: ... R1 R6 6 75 0 Stores tax rate 13 68 5 68 5 Enters quantity and price of first item on invoice t 890 50 AMOUNT for first item 60 11 TAX for first item 950 61 TOTAL for first item 18 72 9 72 9 Enters quantity and price of second item on invoice t 1 312 20 AMOUNT for second item 88 57 TAX for second item 1 400 77 TOTAL for second item 24 85 85 Enters quantity and price of third item on invoice t 2 04...

Page 124: ...automatically halted when the program executes a t instruction To resume executing the program from the program line at which execution was halted press t Example Replace the program above by one containing t instructions instead of gu instructions Keystrokes RPN mode Display fs Sets calculator to Program mode fCLEARÎ 000 Clears program memory 001 20 t 002 31 Stops program execution to display AMO...

Page 125: ...e program first set the appropriate mode by pressing f or f and then do the following Keystrokes Display fs 6 370 52 Sets calculator to Run mode fCLEAR 0 00 Clears registers R1 through R6 13 68 5 68 5 First item t 890 50 AMOUNT for first item t 60 11 TAX for first item t 950 61 TOTAL for first item 18 72 9 72 9 Second item t 1 312 20 AMOUNT for second item t 88 57 TAX for second item t 1 400 77 TO...

Page 126: ...t to display the current program line by pressing fs if your program has halted at one of several t instructions in your program and you want to determine which one that is To continue executing the program afterward 1 Press fs to set the calculator back to Run mode 2 If you want to resume execution from the program line at which execution halted rather than from line 000 press gi followed by thre...

Page 127: ...g its three digit line number into the program line containing the i instruction When the i instruction is executed program execution branches or goes to the program line specified and then continues sequentially as usual You have already seen a common use of branching the gi000 instruction that is stored in program memory after the program you key in transfers execution to program line 000 A i in...

Page 128: ...hen you start running the program Before running the program we ll initialize it by storing the required data in the financial registers just as we would do if we were amortizing a single payment manually We ll run the program for a 150 000 mortgage at 4 75 for 30 years and we ll key 1 into the display just before running it in order to amortize monthly payments For the first two passes through th...

Page 129: ...be amortized can be recalled to the display before the f instruction in line 003 is executed fs 0 00 Sets calculator to Run mode Display shown assumes no results remain from previous calculations fCLEARG 0 00 Clears financial registers 30gA 360 00 Enters n 4 75gC 0 40 Enters i 150000 150 000 00 Enters PV g 150 000 00 Sets payment to End P 782 47 Calculates the monthly payment 0n 0 00 Reset n to z...

Page 130: ...his is the end of the first pass through the loop 188 72 Ê 002 45 0 Line 002 0 Program execution has branched to the beginning of the loop for the second pass through it 1 00 Ê 003 42 11 Line 003 f 593 00 Portion of second month s payment applied to interest Ê 004 43 31 Line 004 gu 593 00 Ê 005 34 Line 005 189 47 Portion of second month s payment applied to principal Ê 006 43 31 Line 006 gu 189 47...

Page 131: ...than or equal to the number in the Y register represented by the y in the key symbol As discussed in Appendix A the number in the X register is simply the number that would if the calculator were in Run mode be currently in the display and the number in the Y register is the number that would if the calculator were in Run mode have been in the display when was pressed For example pressing 4 5 woul...

Page 132: ...xample The following program calculates income tax at a rate of 20 on incomes of 20 000 or less and 25 on incomes of more than 20 000 To conserve program lines the program assumes that the test value 20 000 has been stored in register R0 and the tax rates 20 and 25 have been stored in registers R1 and R2 respectively Note If a program requires that certain numbers be in the X and Y registers when ...

Page 133: ...gister and place the test value into the Y register This is necessary because when either the 2 instruction in line 005 or the 1 instruction in line 007 is executed the number in the X register is moved into the Y register if the instruction were not included the test value 20 000 rather than the income would be in the Y register when the b instruction in line 008 is executed Keystrokes RPN mode D...

Page 134: ...re that it will be in the X register when the 0 instruction in program line 002 is executed This instruction will place the test value 20 000 in the X register and move the income into the Y register The instruction in program line 003 will exchange the numbers in the X and Y registers that is it will place the income back into the X register and place the test value into the Y register This is ne...

Page 135: ... 25 Divides tax rate by 100 011 36 Calculates tax fs 190 22 Sets calculator to Run mode Display shows results of running of previous program Now we ll store the required numbers in registers R0 R1 and R2 then we ll run the program using Ç so that we can check that the branching occurs properly It s good practice with programs containing conditional test instructions to check that the program branc...

Page 136: ...true so program execution continued with line 004 gi007 15 000 00 Ê 007 45 1 Line 007 1 20 00 20 tax rate has been recalled to X register moving income to Y register Ê 008 25 Line 008 b 3 000 00 20 of 15 000 3 000 20000 20 000 Keys income equal to test value into display and X register Ê 001 45 0 Line 001 0 20 000 00 Test value has been recalled to X register moving income to Y register Ê 002 34 L...

Page 137: ...est value into display and X register Ê 001 45 0 Line 001 0 20 000 00 Test value has been recalled to X register moving income to Y register Ê 002 34 Line 002 25 000 00 Income has been placed in X register and test value has been placed in Y register Ê 003 43 34 Line 003 go 25 000 00 Ê 005 45 2 Condition tested by o was false so program execution skipped the next line and continued at line 005 2 2...

Page 138: ...02 0 20 000 00 Test value has been recalled to X register moving income to Y register Ê 003 34 Line 003 15 000 00 Income has been placed in X register and test value has been placed in Y register Ê 004 20 Line 004 15 000 00 Ê 005 43 34 Line 005 go 15 000 00 Ê 006 43 33 009 Condition tested by o was true so program execution continued with line 006 gi009 15 000 00 Ê 009 45 1 Line 009 1 20 00 20 tax...

Page 139: ... to Y register Ê 003 34 Line 003 20 000 00 Income has been placed in X register and test value has been placed in Y register Ê 004 20 Line 004 20 000 00 Ê 005 43 34 Line 005 go 20 000 00 Ê 006 43 33 009 Condition tested by o was true so program execution continued with line 006 gi009 20 000 00 Ê 009 45 1 Line 009 1 20 00 20 tax rate has been recalled to X register moving income to Y register Ê 010...

Page 140: ...gister Ê 003 34 Line 003 25 000 00 Income has been placed in X register and test value has been placed in Y register Ê 004 20 Line 004 25 000 00 Ê 005 43 34 Line 005 go 25 000 00 Ê 007 45 2 Condition tested by o was false so program execution skipped the next line and continued at line 007 2 25 00 25 tax rate has been recalled to X register moving income to Y register Ê 008 43 33 010 Line 008 gi01...

Page 141: ...ng the instruction to be changed 3 Key in the new instruction For example to change the instruction stored in program line 005 press gi 004 then key in the new instruction that is to be stored in program line 005 The instruction previously stored in line 005 will be replaced it is not automatically bumped into line 006 Example With the last program from the preceding section still stored in the ca...

Page 142: ...nto program line 007 replacing the 2 instruction previously there Ê 008 43 33 010 Shows that instruction in program line 008 has not been changed fs 6 250 00 Sets calculator back to Run mode Display shown assumes results remain from last example in preceding section 2 6 25 00 Copies tax rate from R2 into R6 Adding Instructions at the End of a Program To add one or more instructions at the end of t...

Page 143: ...one by changing the sign of the tax to make it negative and then adding it to the income You could do this as follows Keystrokes RPN mode Display fs Sets calculator to Program mode gi 008 008 25 Sets calculator to last line keyed into program memory 009 30 Keys new instruction into program line 009 fs 25 00 Sets calculator back to Run mode 15000t 12 000 00 Net income after 20 tax is subtracted fro...

Page 144: ...use the method described below under Adding Instructions by Branching That method basically involves branching to the new instructions which are stored at the end of program memory then branching back to the program line immediately following the line from which you branched out Adding instructions by branching is not so simple as adding instructions by replacement however it generally will requir...

Page 145: ... insert a t instruction before the program calculates net income after tax so that the program will display the amount of the tax before displaying the net income after tax The program should be modified by making the changes below Keystrokes RPN mode Display fs Sets calculator to Program mode gi 008 008 25 Sets calculator to last program line to be executed which contains the b instruction t 009 ...

Page 146: ...t step This i instruction will replace whatever instruction was already stored there but that instruction will be keyed back into program memory to be executed just after the new instructions in step 7 3 Press gi followed by three digits that specify the second line after the last line you keyed into program memory Branching to the second line rather than to the first is necessary because the firs...

Page 147: ...ing the original income keyed in by storing 7 500 in register R3 and adding the following instructions between lines 000 and 001 the added lines are the same in RPN and ALG modes 3 gogi000 Since there are more than four instructions between and including the first line to be executed after the added instructions line 001 and the last line you keyed into program memory line 010 in RPN and line 016 ...

Page 148: ...in line 001 by gi012 instruction gi002 017 43 33 002 Branches back to second line line 002 following point at which new instructions are being added fs 12 000 00 Sets calculator back to Run mode 7500 3 7 500 00 Stores test value in register R3 6500t 6 500 00 Runs program for income less than 7 500 Display shows original income keyed in indicating that tax is zero 15000t 3 000 00 Tax on 15 000 inco...

Page 149: ...ction keyed in next will be stored as the last line of the current program gi000 017 43 33 000 Ends the current program with a gi000 3 018 45 3 019 34 go 020 43 34 gi000 021 43 33 000 Added instructions 9 022 44 9 Keys in instruction immediately following point at which new instructions are being added This instruction was replaced in line 001 by gi018 instruction gi002 023 43 33 002 Branches back...

Page 150: ...ows program still works for an income greater than 7 500 and less than 20 000 The following illustration of the edited RPN program shows how program execution branches to the instructions added at the end of program memory then branches back While the actual program in ALG mode is different the illustration does indicate the method used ...

Page 151: ...e already two or more programs stored in program memory skip step 3 and proceed with step 4 3 Press gi000 This automatically converts a data storage register into seven additional lines of program memory if there was not already a i000 instruction remaining at the end of program memory and it ensures that program execution will branch to line 000 after the first program is run 4 Key the program in...

Page 152: ...ates it from the first program by doing step 3 in the procedure above Furthermore since this program does not end with a loop we ll do steps 5 and 6 too Keystrokes RPN mode Display fs Sets calculator to Program mode gi 017 017 43 33 002 Sets calculator to last line keyed into program memory gi000 018 43 33 000 Ensures that second program is separated from first by i000 019 36 2 020 2 5 021 5 b 022...

Page 153: ...ortization program from Section 9 page 127 Since there are already two programs stored in program memory we ll skip step 3 in the procedure above Furthermore since the amortization program ends with a loop we ll skip steps 5 and 6 When the amortization program was stored at the beginning of program memory the i instruction at the end of the program branched to the 0 instruction in line 002 In the ...

Page 154: ...43 31 032 34 gu 033 43 31 gi029 034 43 33 029 Keys in program Keystrokes ALG mode Display fs Sets calculator to Program mode gi 033 033 43 33 025 Sets calculator to last line keyed into program memory 0 034 44 0 0 035 45 0 f 036 42 11 gu 037 43 31 038 34 gu 039 43 31 gi035 040 43 33 035 Keys in program ...

Page 155: ... the office supplies program now stored in the calculator beginning at program line 019 in RPN mode and line 025 in ALG mode for the typewriter listing for 625 Keystrokes RPN mode Display fs 12 000 00 Sets calculator to Program mode gi019 12 000 00 Sets calculator to first line of program to be executed 625t 473 75 Net cost of typewriter Keystrokes ALG mode Display fs 12 000 00 Sets calculator to ...

Page 156: ......

Page 157: ...Part III Solutions ...

Page 158: ...er the periodic payment amount of the loan a Key in the total number of payment periods press n b Key in the periodic interest rate as a percentage press c Key in the mortgage amount press d To obtain the periodic payment amount press P 3 Calculate and key in the actual net amount disbursed RPN Mode z If fees are stated as a percentage of the mortgage amount points recall the mortgage amount key i...

Page 159: ...in the number of periods per year then press µ 5 ALG To obtain the annual nominal percentage rate press µ Key in the number of periods per year then press Example 1 A borrower is charged 2 points for the issuance of his mortgage If the mortgage amount is 160 000 for 30 years and the interest rate is 5 5 per year with monthly payments what true annual percentage rate is the borrower paying One poin...

Page 160: ... 46 Monthly payment calculated 750 750 159 250 00 Effective mortgage amount into PV 0 46 Monthly interest rate calculated 12 12 5 54 Annual percentage rate Example 3 Again using the information given in example 1 what is the APR if the mortgage fee is stated as 2 points plus 750 Keystrokes RPN mode Keystrokes ALG mode Display f f g g fCLEARG fCLEARG 30gA 30gA 360 00 Months into n 5 5gC 5 5gC 0 4...

Page 161: ...ress g and fCLEARG 2 Key in the total number of periods until the balloon payment or prepayment occurs press n If there is no balloon payment key in total number of payments and press n 3 Key in the desired periodic interest rate yield and press 4 Key in the periodic payment amount press P 5 Key in the balloon payment amount and press M If there is no balloon payment go to step 6 6 Press to obtai...

Page 162: ...ield is 12 Since the payment amount is not given it must be calculated Keystrokes RPN mode Keystrokes ALG mode Display f f g fCLEARG 26gA g fCLEARG 26gA 312 00 Months into n 6 5gC 6 5gC 0 54 Percent monthly interest rate into i 249350Þ P 249350Þ P 1 657 97 Monthly payment to be received calculated 12gC 12gC 1 00 Desired monthly interest rate into i 158 361 78 Purchase price to achieve the desire...

Page 163: ...s 5 Key in the balloon payment amount then press M If there is no balloon payment go to step 6 6 Press to obtain the yield per period 7 RPN Key in the number of periods per year and press to obtain the nominal annual yield 7 ALG Press Key in the number of periods per year and press to obtain the nominal annual yield Example 1 An investor wishes to purchase a 300 000 mortgage taken out at 6 for 21 ...

Page 164: ...nth calculated 12 12 7 20 Percent annual yield Example 2 Using the same information given in example 1 calculate the annual yield if the loan is to be paid in full at the end of the fifth year from original issuance In this case both the payment amount and the balloon must be calculated since they are not given Keystrokes RPN mode Keystrokes ALG mode Display f f g fCLEARG 21gA g fCLEARG 21gA 252...

Page 165: ... of return on the proposed investment This yield may be compared with the yield obtained by renting a residence and investing the down payment and monthly payment differences in a savings account or other investment opportunity This program takes into account the tax advantages obtained by a home owner on property taxes and mortgage interest First the program computes the Net Cash Proceeds upon Re...

Page 166: ...05 45 11 0 006 44 0 0 006 44 0 007 45 13 007 45 13 fCLEARG 008 42 34 fCLEARG 008 42 34 1 009 45 1 009 30 010 30 1 010 45 1 011 13 011 13 2 012 45 2 2 012 45 2 gA 013 43 11 gA 013 43 11 3 014 45 3 3 014 45 3 gC 015 43 12 gC 015 43 12 P 016 14 P 016 14 0 017 0 0 017 0 n 018 11 n 018 11 0 019 45 0 0 019 45 0 1 020 1 020 20 2 021 2 1 021 1 FV is repeated in the program twice to ensure that it is compu...

Page 167: ...5 10 z 026 10 n 026 45 11 4 027 45 4 027 40 028 40 4 028 45 4 0 029 45 48 0 029 20 b 030 25 0 030 45 48 0 4 031 45 4 b 031 25 032 30 032 30 5 033 45 5 4 033 45 4 034 30 034 30 8 035 45 8 5 035 45 5 036 40 036 40 P 037 45 14 8 037 45 8 038 40 038 40 P 039 14 P 039 45 14 1 040 45 48 1 P 040 14 7 041 45 7 1 041 45 48 1 b 042 25 042 30 043 30 7 043 45 7 044 45 13 b 044 25 ...

Page 168: ...5 1 050 40 Þ 050 16 Þ 051 16 051 30 052 13 6 052 45 6 053 12 053 13 gC 054 45 43 12 054 12 t 055 31 gC 055 45 43 12 9 056 45 9 t 056 31 gC 057 43 12 9 057 45 9 M 058 15 gC 058 43 12 fs M 059 15 fs REGISTERS n Period i Apprec PV Price PMT Used FV Used R0 Period R1 Dwn Pmt R2 Life R3 i Mtg R4 Taxes Mo R5 Improve mo R6 Closing C R7 Comm R8 Rent R9 Savings i R 0 Tax Bracket R 1 Market V ...

Page 169: ...use under consideration then press 15 Press t to compute the net proceeds from the sale of the house A negative value indicates money lost 16 Press t to compute the yield on your investment in the house 17 Press t to compute the value of a savings account or other investment 18 Compare the value of the hypothetical savings account to the net proceeds of the sale of the house Examine the sign and m...

Page 170: ...onth An alternative would be to rent a similar dwelling at 900 per month and to invest the difference between the purchase cost and rent at 3 interest Your personal income tax rate marginal is 25 Federal and 5 State Which alternative is more financially attractive Keystrokes RPN mode Keystrokes ALG mode Display f f g g fCLEARH fCLEARH 0 00 7000 1 7000 1 7 000 00 Down payment 30 2 30 2 30 00 Life...

Page 171: ...gh 77 Example 1 You have just inherited 20 000 and wish to put some of it aside for your daughter s college education You estimate that when she is of college age 9 years from now she will need 7 000 at the beginning of each year for 4 years for college tuition and expenses You wish to establish a fund which earns 6 annually How much do you need to deposit in the fund today to meet your daughter s...

Page 172: ...hey start at some time in the future The cash flow diagram from the investor s viewpoint looks like this To find today s present value of the cash flows assuming a desired yield the NPV technique may be used Refer to pages 73 through 77 Example 2 A 2 year lease calls for monthly payments at the beginning of the month of 500 per month for the first 6 months 600 per month for the next 12 months and ...

Page 173: ...Section 12 Real Estate and Lending 173 Keystrokes RPN mode Keystrokes ALG mode Display 13 5gC 13 5gC 1 13 Monthly interest rate fl fl 12 831 75 Amount to invest to achieve a 13 5 yield ...

Page 174: ...in the first and last years are computed as fractions of a full year s depreciation Straight Line Depreciation The following hp 12c platinum program calculates the straight line depreciation for the year desired with the acquisition date occurring at any time during the year KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 1 001 1 z 001 10 2 002 2 1 002 1 z 003...

Page 175: ...8 13 018 45 13 n 019 45 11 019 30 1 020 45 1 020 34 021 30 021 13 n 022 11 n 022 45 11 0 023 45 0 023 30 gm 024 43 35 1 024 45 1 gi035 025 43 33 035 n 025 11 2 026 45 2 0 026 45 0 gu 027 43 31 gm 027 43 35 0 028 45 0 gi038 028 43 33 038 fV 029 42 23 2 029 45 2 t 030 31 gu 030 43 31 1 031 1 0 031 45 0 0 032 44 40 0 fV 032 42 23 2 033 44 40 2 t 033 31 gi026 034 43 33 026 1 034 1 2 035 45 2 0 035 44 ...

Page 176: ... 31 3 040 45 3 040 45 13 gi030 041 43 33 030 041 30 fs M 042 45 15 043 36 3 044 45 3 gi033 045 43 33 033 fs REGISTERS n Life i Unused PV Dep Value PMT Unused FV Salvage R0 Used R1 Mos 12 R2 Counter R3 1st Yr Dep R4 R 4 Unused 1 Key in the program 2 Press fCLEARG 3 Key in the book value then press 4 Key in the salvage value then press M 5 Key in the life in years an integer then press n ...

Page 177: ... months in the first calendar year is less than 12 the amount of depreciation in the 1st year will be less than a full year s depreciation The actual number of years that depreciation will occur is equal to the life 1 For example a drill has a life of 3 years and is purchased 3 months before the year end The following time diagram shows that depreciation will occur over 4 calendar years Example 1 ...

Page 178: ...ng depreciable value t t 2 00 5 000 00 118 333 33 Second year depreciation remaining depreciable value t t 3 00 5 000 00 Third year depreciation 3 gi000 3 gi000 11 666 67 Total depreciation through third year fCLEARG fCLEARG 11 666 67 125000 125000 125 000 00 Book value 25n 25n 25 00 Life 25 25 25 00 Year desired 4t 4t 25 00 5 000 00 3 333 33 Twenty fifth year depreciation remaining depreciable va...

Page 179: ... value 5n 5n 5 00 Life 1 1 1 00 4 5t 4 5t 1 00 504 75 First year depreciation Declining Balance Depreciation The following hp 12c platinum program calculates the declining balance depreciation for the year desired with the acquisition date occurring at any time during the year KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 1 001 1 z 001 10 2 002 2 1 002 1 z 0...

Page 180: ...34 016 36 017 30 3 017 44 3 018 13 018 45 13 0 019 45 0 019 30 gm 020 43 35 020 34 gi031 021 43 33 031 021 13 2 022 45 2 0 022 45 0 gu 023 43 31 gm 023 43 35 0 024 45 0 gi034 024 43 33 034 f 025 42 25 2 025 45 2 t 026 31 gu 026 43 31 1 027 1 0 027 45 0 0 028 44 40 0 f 028 42 25 2 029 44 40 2 t 029 31 gi022 030 43 33 022 1 030 1 2 031 45 2 0 031 44 40 0 gu 032 43 31 2 032 44 40 2 033 45 13 gi025 03...

Page 181: ...45 15 039 36 3 040 45 3 gi029 041 43 33 029 fs REGISTERS n Life i Factor PV Dep Value PMT Unused FV Salvage R0 Used R1 Mos 12 R2 Counter R3 1st Yr Dep R4 R 4 Unused 1 Key in the program 2 Press fCLEARG 3 Key in the book value then press 4 Key in the salvage value then press M 5 Key in the declining balance factor as a percentage then press 6 Key in the life in years an integer then press n ...

Page 182: ...ss for the remaining depreciable value for the next year Repeat this step for the following years 10 For a new case press gi000 and return to step 2 Example An electron beam welder which costs 50 000 is purchased 4 months before the end of the accounting year What will the depreciation be during the first full accounting year year 2 if the welder has a 6 year depreciable life a salvage value of 8 ...

Page 183: ...for the year desired with the acquisition date occurring at any time during the year KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 1 001 1 z 001 10 2 002 2 1 002 1 z 003 10 2 003 2 1 004 44 1 004 36 005 34 1 005 44 1 2 006 44 2 006 34 1 007 1 2 007 44 2 008 30 008 30 0 009 44 0 1 009 1 1 010 1 010 36 fÝ 011 42 24 0 011 44 0 1 012 45 1 1 012 1 013 20 fÝ 013 4...

Page 184: ...m 024 43 35 1 024 45 1 gi035 025 43 33 035 n 025 11 2 026 45 2 0 026 45 0 gu 027 43 31 gm 027 43 35 0 028 45 0 gi038 028 43 33 038 fÝ 029 42 24 2 029 45 2 t 030 31 gu 030 43 31 1 031 1 0 031 45 0 0 032 44 40 0 fÝ 032 42 24 2 033 44 40 2 t 033 31 gi026 034 43 33 026 1 034 1 2 035 45 2 0 035 44 40 0 gu 036 43 31 2 036 44 40 2 037 45 13 gi029 037 43 33 029 M 038 45 15 2 038 45 2 039 30 gu 039 43 31 3...

Page 185: ... 45 15 043 36 3 044 45 3 gi033 045 43 33 033 fs REGISTERS n Life i Unused PV Dep Value PMT Unused FV Salvage R0 Used R1 Mos 12 R2 Counter R3 1st Yr Dep R4 R 4 Unused 1 Key in the program 2 Press fCLEARG 3 Key in the book value then press 4 Key in the salvage value then press M 5 Key in the life in years an integer then press n ...

Page 186: ...depreciation then if desired press for the remaining depreciable value for the next year Repeat this step for the following years 9 For a new case press gi000 and return to step 2 Example A commercial movie camera is purchased for 12 000 If maintained properly the camera has a useful life expectancy of 25 years with 500 salvage value Using the sum of the years digits method what is the amount of d...

Page 187: ...lly switches to straight line depreciation at the appropriate time The crossover point is the end of the year in which the declining balance depreciation last exceeds or equals the amount of straight line depreciation The straight line depreciation is determined by dividing the remaining depreciable value by the remaining useful life Given the desired year and the number of months in the first yea...

Page 188: ...d 011 33 0 012 44 30 0 d 012 33 2 013 44 2 0 013 44 0 3 014 44 3 1 014 1 f 015 42 25 0 015 44 30 0 6 016 45 6 2 016 44 2 017 20 3 017 44 3 1 018 44 1 f 018 42 25 019 45 13 019 20 020 34 6 020 45 6 021 30 021 36 022 13 1 022 44 1 023 36 023 45 13 gF 024 43 40 024 30 025 34 025 34 M 026 45 15 026 13 027 30 1 027 45 1 028 34 028 45 13 0 029 45 0 029 30 1 030 1 M 030 45 15 ...

Page 189: ...043 036 43 33 043 d 037 33 d 037 33 t 038 31 d 038 33 1 039 1 1 039 1 2 040 44 40 2 gu 040 43 31 0 041 44 30 0 d 041 33 f 042 42 25 t 042 31 1 043 44 40 1 1 043 1 5 044 44 5 2 044 44 40 2 045 45 13 0 045 44 30 0 M 046 45 15 f 046 42 25 047 30 1 047 44 40 1 4 048 45 4 5 048 44 5 z 049 10 049 45 13 go 050 43 34 050 30 gi053 051 43 33 053 M 051 45 15 gi065 052 43 33 065 z 052 10 d 053 33 4 053 45 4 0...

Page 190: ...30 0 060 45 0 061 13 go 061 43 34 1 062 1 gi091 062 43 33 091 4 063 44 30 4 063 45 13 gi040 064 43 33 040 064 30 4 065 45 4 5 065 45 5 n 066 11 066 13 0 067 0 1 067 1 6 068 44 6 4 068 44 30 4 1 069 1 gi044 069 43 33 044 2 070 44 30 2 4 070 45 4 0 071 44 40 0 n 071 11 5 072 45 5 0 072 0 1 073 44 30 1 6 073 44 6 3 074 45 3 1 074 1 fV 075 42 23 2 075 44 30 2 1 076 44 40 1 0 076 44 40 0 1 077 1 5 077 ...

Page 191: ... 1 0 083 44 30 0 go 084 43 34 2 084 44 40 2 gi074 085 43 33 074 3 085 44 40 3 d 086 33 d 086 33 d 087 33 0 087 45 0 2 088 45 2 1 088 1 gu 089 43 31 go 089 43 34 d 090 33 gi079 090 43 33 079 t 091 31 d 091 33 6 092 45 6 d 092 33 gm 093 43 35 2 093 45 2 gi074 094 43 33 074 gu 094 43 31 gi058 095 43 33 058 d 095 33 fs t 096 31 6 097 45 6 gm 098 43 35 gi079 099 43 33 079 gi063 100 43 33 063 fs ...

Page 192: ...o see the total depreciation through the current year 11 Continue pressing t to find the amount of depreciation for the successive years Steps 9 and 10 may be repeated for each year 12 For a new case press gi000 and return to step 2 Example An electronic instrument is purchased for 11 000 with 6 months remaining in the current fiscal year The instrument s useful life is 8 years and the salvage val...

Page 193: ...maining depreciable value t t 2 00 2 406 25 Second year depreciation t t 3 00 1 804 69 Third year depreciation t t 4 00 1 353 51 Fourth year depreciation t t 5 00 1 015 14 Fifth year depreciation t t 6 00 761 35 Sixth year depreciation t t 7 00 713 62 Seventh year depreciation 1 1 9 429 56 Total depreciation through the seventh year t t 8 00 713 63 Eight year depreciation t t 9 00 356 81 Ninth yea...

Page 194: ... excess depreciation ALG Mode 1 Calculate the total depreciation then press gØ 2 Key in the depreciable amount cost less salvage then press z Key in the useful life of the asset in years then press Key in the number of years in the income projection period then press gÙ to get the total straight line depreciation charge 3 Press to get the excess depreciation Example What is the excess depreciation...

Page 195: ...nternal rates of return This particular example has three positive real answers 1 86 14 35 and 29 Although mathematically sound multiple answers probably are meaningless as an investment measure This Modified Internal Rate of Return procedure MIRR is one of several IRR alternatives which avoids the drawbacks of the traditional IRR technique The procedure eliminates the sign change problem and the ...

Page 196: ...play f f fCLEARH fCLEARH 0 00 0gJ 0gJ 0 00 First cash flow 100000gK 100000gK 100 000 00 5ga 5ga 5 00 Second through sixth cash flows 0gK5ga 0gK5ga 5 00 Next five cash flows 0gK9ga 0gK9ga 9 00 Next nine cash flows 200000gK 200000gK 200 000 00 Last cash flow 10gCfl 10gCfl 657 152 37 NPV of positive cash flows Þ Þ 657 152 37 20nM 20nM 775 797 83 NFV of positive cash flows 180000Þg J0gK5g a100000Þ gK5...

Page 197: ...roduced are accurate to at least the nearest cent for asset and strike prices under 100 Reference Tony Hutchins 2003 Black Scholes takes over the HP12C HPCC www hpcc org Datafile V22 N3 pp13 21 KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 n 001 45 11 n 001 45 11 002 45 12 002 20 b 003 25 003 45 12 Þ 004 16 b 004 25 g 005 43 22 005 36 M 006 45 15 Þ 006 16 00...

Page 198: ...10 2 021 2 4 021 45 4 5 022 44 5 022 36 z 023 10 g 023 43 23 024 40 z 024 10 6 025 44 6 025 34 3 026 45 3 026 36 027 30 3 027 45 3 3 028 44 3 z 028 10 029 36 2 029 2 030 20 5 030 44 5 gr 031 43 21 031 40 gF 032 43 40 032 34 2 033 2 033 30 z 034 10 6 034 44 6 Þ 035 16 3 035 45 3 g 036 43 22 036 36 037 34 3 037 44 3 3 038 3 g 038 43 20 039 48 z 039 10 0 040 0 2 040 2 ...

Page 199: ...044 1 3 044 45 3 045 40 g 045 43 20 y 046 22 gr 046 43 21 047 20 z 047 10 gF 048 43 40 3 048 3 gF 049 43 40 049 48 1 050 1 0 050 0 8 051 8 0 051 0 7 052 7 6 052 6 053 20 053 40 2 054 2 1 054 1 4 055 4 055 36 056 30 y 056 22 057 20 2 057 44 2 8 058 8 058 20 7 059 7 059 34 060 40 060 36 061 20 1 061 1 062 48 8 062 8 2 063 2 7 063 7 b 064 25 064 20 ...

Page 200: ...34 2 070 45 2 g 077 071 43 33 077 071 40 1 072 1 8 072 8 3 073 44 30 3 7 073 7 Þ 074 16 074 20 3 075 44 20 3 075 34 076 34 076 20 5 077 45 5 077 48 gm 078 43 35 2 078 2 g 089 079 43 33 089 b 079 25 6 080 45 6 080 36 3 081 45 3 3 081 45 3 4 082 45 4 082 34 083 20 3 083 44 3 6 084 44 6 O 084 35 O 085 35 085 34 5 086 44 5 go 086 43 34 087 34 g 093 087 43 33 093 g 028 088 43 33 028 1 088 1 ...

Page 201: ... 091 45 13 3 091 44 20 3 4 092 44 30 4 092 34 093 20 5 093 45 5 6 094 45 6 gm 094 43 35 095 30 g 106 095 43 33 106 4 096 44 40 4 6 096 45 6 4 097 45 4 3 097 45 3 098 34 098 20 5 099 44 5 4 099 45 4 fs 100 36 6 101 44 6 O 102 35 5 103 44 5 104 34 g 037 105 43 33 037 106 34 107 45 13 4 108 44 30 4 109 20 3 110 45 3 111 30 6 112 45 6 ...

Page 202: ...us percentage rate PMT is the standard deviation of the continuous percentage stock return as observed over the time unit For sensible output all inputs should be positive The PMT 0 case can be simulated by using a PMT arbitrarily close to 0 Program Instructions 1 Key in the program 2 Enter the five inputs into the five financial registers These values are preserved by the program a Key in the une...

Page 203: ...play f f 6n 6n 6 00 Time to expiry months 5 5 0 50 Interest rate per month 52 52 52 00 Stock price 20 54P 20 54P 20 54 Volatility per month 45M 45M 45 00 Strike price t t 14 22 Call value 5 89 Put value gAn gAn 0 50 Years to expiry gC gC 6 00 Yearly interest rate P 12gr P P 12grP 71 15 Yearly volatility t t 14 22 Call value unchanged ngA ngA 6 00 Months to expiry gC gC 0 50 Monthly interest rate P...

Page 204: ...s 40 the risk free interest rate is 10 per annum and the volatility is 20 per annum Find Call and Put values Keystrokes RPN mode Keystrokes ALG mode Display f f 5n 5n 0 50 Time to expiry years 10 10 10 00 Interest rate per year 42 42 42 00 Stock price 20P 20P 20 00 Volatility per year 40M 40M 40 00 Strike price t t 4 76 Call value 0 81 Put value ...

Page 205: ... as follows 1 Press g and fCLEARG RPN Mode 2 Key in the total number of payments in the lease then press 3 Key in the total number of payments made in advance then press 0 n 4 Key in or calculate the periodic interest rate as a percentage then press 5 Press 1ÞP 0 6 Key in the initial loan amount then press z to obtain the periodic payment to be received by the lessor ALG Mode 2 Key in the total n...

Page 206: ...f f g g fCLEARG fCLEARG 12 12 12 00 Duration of lease 3 0 n 3 0n 9 00 Number of periodic payments 10gC 10gC 0 83 1ÞP 1ÞP 1 00 0 0 11 64 750 z 750z 64 45 Monthly payment to be received If solving for the payment amount will be done repetitively key in the following hp 12c platinum program KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 g 001 43 8 g 001 43 8...

Page 207: ...d PMT 1 FV 0 R0 n R1 Adv Pmt R2 i R3 Loan R4 R 7 Unused 1 Key in the program 2 Key in the total number of payments in the lease then press 0 3 Key in the total number of payments made in advance then press 1 4 Key in the periodic interest rate as a percentage then press 2 5 Key in the loan amount and press 3 then press t to obtain the periodic payment to be received by the lessor 6 For a new case ...

Page 208: ...achieve a 15 yield Example 3 Using the information from example 1 what monthly payment is necessary to yield the lessor 15 annually if one payment is due at the time of closing Assuming that the previous example was just solved the keystrokes are as follows Keystrokes RPN mode Keystrokes ALG mode Display 1 1t 1 1t 66 86 Monthly payment to be received Since this problem is an annuity due situation ...

Page 209: ...lease then press 3 Key in the total number of payments made in advance then press 0n 4 Key in the periodic payment to be received then press P 5 Press 0 P Then key in the total amount of the loan and press Þ 6 Press to obtain the periodic yield Example 1 A lease has been written to run for 60 months The leased equipment has a value of 25 000 with a 600 monthly payment The lessee has agreed to make...

Page 210: ...platinum program KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 g 001 43 8 g 001 43 8 fCLEARG 002 42 34 fCLEARG 002 42 34 0 003 45 0 0 003 45 0 1 004 45 1 004 30 005 30 1 005 45 1 n 006 11 n 006 11 2 007 45 2 2 007 45 2 P 008 14 P 008 14 3 009 45 3 009 20 Þ 010 16 1 010 45 1 1 011 45 1 011 30 P 012 45 14 3 012 45 3 013 20 013 13 014 40 014 12 015 13 gC 015 ...

Page 211: ...t of the loan then press 3 then press t to obtain the periodic yield 6 For a new case return to step 2 The values changed from the previous case are the only values which need to be re entered Example 2 Using the program solve for yield using the same information given in example 1 Then change the payment to 625 and solve for the yield Keystrokes RPN mode Keystrokes ALG mode Display f f 60 0 60 0 ...

Page 212: ...t necessary to achieve a desired yield KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARΠ000 fCLEARΠ000 g 001 43 8 g 001 43 8 fCLEARG 002 42 34 fCLEARG 002 42 34 0 003 45 0 0 003 45 0 n 004 11 n 004 11 1 005 45 1 1 005 45 1 006 12 006 12 3 007 45 3 3 007 45 3 M 008 15 M 008 15 009 13 009 13 2 010 45 2 010 40 011 40 2 011 45 2 5 012 44 5 012 36 0 013 0 5 013 44 5 M 014 15 0 0...

Page 213: ...36 fs REGISTERS n Used i Interest PV Used PMT 1 FV Residual R0 Pmts n R1 Interest R2 Loan R3 Residual R4 Adv Pmt R5 Used R6 R 6 Unused 1 Key in the program 2 Key in the total number of payments then press 0 3 Key in or calculate the periodic interest rate then press 1 4 Key in the loan amount then press 2 5 Key in the residual value then press 3 6 Key in the total number of payments made in advanc...

Page 214: ... payment is necessary to yield the lessor 15 annually Keystrokes RPN mode Keystrokes ALG mode Display f f 48 0 48 0 48 00 Duration of lease 15 15z 15 00 12z 1 12 1 1 25 Monthly interest rate 22000 2 22000 2 22 000 00 30b 3 30b 3 6 600 00 4 4t 4 4t 487 29 Monthly payment received by lessor Example 2 Using the information from example 1 what would the monthly payments be if the lessor desired a yiel...

Page 215: ... occurs then press ga 4 Key in 0gK then the number of advance payments minus one Then press ga 5 Key in the residual then press gK Then press fL to solve for periodic yield Example Equipment worth 5 000 is leased for 36 months at 145 per month The lessee has agreed to pay the first and last month s payments in advance At the end of the lease the equipment may be purchased for 1 500 What is the ann...

Page 216: ...216 Section 14 Leasing Keystrokes RPN mode Keystrokes ALG mode Display fL12 fL 12 18 10 Annual yield to lessor ...

Page 217: ...he effective annual interest rate ALG Mode 2 Key in the annual nominal rate as a percentage 3 Press z Key in the number of compounding periods per year then press ÞP Then key in the number of compounding periods per year and press n 4 Press M to obtain the effective annual interest rate Example 1 What is the effective annual interest rate if the annual nominal rate of 5 25 is compounded quarterly ...

Page 218: ...ISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 g 001 43 8 g 001 43 8 fCLEARG 002 42 34 fCLEARG 002 42 34 n 003 11 n 003 11 z 004 10 004 34 005 12 z 005 10 Þ 006 16 006 34 P 007 14 007 12 M 008 15 Þ 008 16 fs P 009 14 M 010 15 fs REGISTERS n Periods i Nom Rate n PV 0 PMT Used FV Eff Rate R0 R 9 Unused ...

Page 219: ... monthly Keystrokes RPN mode Keystrokes ALG mode Display 5 25 5 25 5 25 12t 12t 5 38 Percent effective interest rate Effective Rate Converted to Nominal Rate Given an effective interest rate and the number of compounding periods per year this routine calculates the nominal interest rate 1 Press fCLEARG 2 Key in the number of periods per year then press n 3 Key in 100 then press RPN Mode 4 Key in t...

Page 220: ...ominal interest rate Continuous Rate Converted to Effective Rate This procedure converts a continuous annual interest rate to the effective rate 1 RPN Press 1 1 ALG Press 1 2 Key in the continuous rate as a percentage then press b 3 Press g à Example What is the effective rate resulting from a 5 25 passbook rate with continuous compounding Keystrokes RPN mode Keystrokes ALG mode Display f f 1 5 25...

Page 221: ...ing program solves for the price given the yield or for the yield given the price of a semiannual coupon bond which is calculated on a 30 360 day basis and is held for more than six months KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 fCLEARG 001 42 34 fCLEARG 001 42 34 g 002 43 7 g 002 43 7 2 003 45 2 2 003 45 2 2 004 2 z 004 10 z 005 10 2 005 2 P 006 14 P ...

Page 222: ...19 43 24 1 020 1 1 020 1 021 34 021 30 022 30 022 34 P 023 45 14 023 20 024 20 P 024 45 14 6 025 44 6 025 36 0 026 45 0 6 026 44 6 gm 027 43 35 0 027 45 0 g 039 028 43 33 039 gm 028 43 35 2 029 2 g 041 029 43 33 041 z 030 10 z 030 10 031 12 2 031 2 032 13 032 12 6 033 45 6 033 13 034 34 6 034 45 6 Þ 035 16 035 34 6 036 45 6 Þ 036 16 037 30 037 30 g 000 038 43 33 000 6 038 45 6 ...

Page 223: ...PV Price PMT Coupon 2 FV Red Cpn 2 R0 Yield R1 Price R2 Coupon R3 Dset R4 Dmat R5 Redemption R6 Accrued Int R7 R 3 Unused 1 Key in the program 2 If the C status indicator is not displayed press É 3 Key in the annual coupon interest rate as a percentage then press 2 4 Key in the settlement date MM DDYYYY then press 3 5 Key in the maturity date MM DDYYYY then press 4 6 Key in the redemption value as...

Page 224: ... yield to maturity For a new case return to step 3 Note that only those values which have been changed need to be reentered and stored Example 1 What price should you pay on August 28 2004 for a 5 5 bond computed with a 30 360 basis that matures on June 1 2008 if you want a yield of 4 75 What price should you pay for a yield of 4 5 This problem assumes a redemption value of 100 Keystrokes RPN mode...

Page 225: ...al price paid Example 2 The market is quoting 105 for the bond described in example 1 What yield will that provide What would be the yield to maturity if 104 were the quoted price Keystrokes RPN mode Keystrokes ALG mode Display 104 74 From previous example 0 0 0 0 0 00 105 1t 105 1t 4 05 Yield at 105 calculated 104 1t 104 1t 4 33 Yield at 104 calculated ...

Page 226: ...a 30 360 day basis KEYSTROKES RPN mode DISPLAY KEYSTROKES ALG mode DISPLAY fs fs fCLEARÎ 000 fCLEARÎ 000 fCLEARG 001 42 34 fCLEARG 001 42 34 g 002 43 8 g 002 43 8 0 003 45 0 0 003 45 0 n 004 11 n 004 11 2 005 45 2 2 005 45 2 P 006 14 P 006 14 1 007 45 1 1 007 45 1 008 12 008 12 3 009 45 3 3 009 45 3 M 010 15 M 010 15 011 13 011 13 5 012 45 5 5 012 45 5 Æ 013 26 013 30 6 014 6 Æ 014 26 Þ 015 16 6...

Page 227: ...45 6 7 021 44 7 4 022 45 4 6 022 45 6 gÒ 023 43 26 4 023 45 4 7 024 45 7 gÒ 024 43 26 z 025 10 z 025 10 n 026 11 7 026 45 7 0 027 0 n 027 11 P 028 14 0 028 0 M 029 15 P 029 14 Þ 030 16 M 030 15 n 031 45 11 n 031 45 11 2 032 45 2 032 20 Þ 033 16 2 033 45 2 034 20 Þ 034 16 t 035 31 035 40 036 30 t 036 31 fs 037 34 038 36 Þ 039 16 fs ...

Page 228: ...t of the annual coupon then press 2 5 Key in the redemption value then press 3 6 Key in the settlement purchase date then press 4 7 Key in the date of the next coupon then press 5 8 Press t to obtain the amount of accrued interest 9 Press t to determine the price of the bond 10 For a new case return to step 2 Example What is the price and accrued interest of a 20 year Eurobond with annual coupons ...

Page 229: ...eystrokes RPN mode Keystrokes ALG mode Display 100 3 100 3 100 00 Redemption value 8 152004 4 8 152004 4 8 15 Settlement date 12 012004 5 12 012004 5 12 01 Next coupon date t t 4 58 Accrued interest t t 94 75 Purchase price ...

Page 230: ......

Page 231: ...Appendices ...

Page 232: ... s used in calculations The Z and T registers are used primarily for the automatic retention of intermediate results during chain calculations as described in section 1 Before we discuss the details of the stack operation let s take a quick look at how the stack is used in a simple arithmetic calculation and in a chain calculation For each key pressed in the keystroke sequence the diagram illustra...

Page 233: ... sections if two numbers are being keyed in for a two number function such as you press between the numbers to separate them The following diagram illustrates what happens in the stack when you enter the numbers 10 and 3 to calculate for example 10 3 Assume that the stack registers have been already loaded with the numbers shown as the result of previous calculations When a digit is keyed into the...

Page 234: ...ter When a number is entered into the displayed X register either from the keyboard from a storage register using or from the LAST X register using F the stack usually lifts first The stack does not lift if the last key pressed before a number is entered was one of the following O _ or If one of these keys was the last key pressed the number in the displayed X register is replaced when a new numbe...

Page 235: ... and number alteration functions y r e B Ñ and T use only the number in the displayed X register When the key is pressed the function is performed upon the number in the X register and the answer is then placed into the X register The stack does not lift so the number formerly in the X register does not get copied into the Y register but this number is copied into the LAST X register The numbers i...

Page 236: ...merly in the X register is copied into the LAST X register and the stack drops When the stack drops the number in the Z register is copied into the Y register and the number in the T register is copied into the Z register but also remains in the T register The diagram on the next page illustrates the stack operation when 8 2 is calculated Assume that the stack and LAST X registers have already bee...

Page 237: ...d calendar or financial function key is pressed The symbols x y z and t represent the number that was in the corresponding register X Y Z or T respectively at the time the function key was pressed Register D Ò Ï n P M l L T t t x z y Z t z INT365 y x number of payments Y z ΔDYS30 day PV x PMTPRIN X DATE ΔDYSactual INT360 n i PV PMT FV NPV IRR PMTINT ...

Page 238: ...AST X Register and the Key The number in the displayed X register is copied into the LAST X register whenever any of the following function keys is pressed z y q r B T Ñ _ Q R e b à Z D Ò Pressing gF lifts the stack unless O _ or was the last key pressed as described on page 234 then copies the number from the LAST X register into the displayed X register The number remains also in the LAST X regi...

Page 239: ... free Virtually every chain calculation you are likely to encounter can be done using only the four stack registers However to avoid having to store an intermediate result in a storage register you should begin every chain calculation at the innermost number or pair of parentheses and then work outward just as you would if you were doing the calculation manually that is using pencil and paper For ...

Page 240: ...those years Keystrokes RPN mode Display 2 2 00 Enters constant into Y Z and T registers 84000 84 000 Enters base amount into displayed X register 168 000 00 Annual sales after first year 336 000 00 Annual sales after second year 672 000 00 Annual sales after third year In the example above the constant was repeatedly multiplied by the result of the previous operation which was already in the displ...

Page 241: ...into Y Z and T registers 15 15 Enters first quantity into displayed X register 65 70 Cost of a package of 15 O75 75 Clears display and enters second quantity into displayed X register 328 50 Cost of a package of 75 O250 250 Clears display and enters third quantity into displayed X register 1 095 00 Cost of a package of 250 You may want to compare this method of arithmetic calculations with constan...

Page 242: ...nly allowing you to correct an erroneous entry by keying in a correct number The second press of O will clear any pending operations as well Pressing the key is another way to ensure that there are no pending operations before beginning a new calculation Simple Arithmetic Calculations in ALG Mode To calculate 21 1 23 8 Keystrokes ALG mode Display OO 0 00 Clears any pending operations 21 1 21 10 En...

Page 243: ...and then press Þ z To change the sign of an already displayed number press Þ Keystrokes ALG mode Display OO 0 00 Clears any pending operations 75Þ 75 Changes the sign of 75 7 1 532 50 Multiplies 75 by 7 1 Chain Calculations in ALG Mode To do a chain calculation you don t need to press after each operation but only at the very end For instance to calculate 360 12 x 750 you can enter either z 750 12...

Page 244: ... in general it changes the value in LAST X However in RPN mode gF always lifts the stack and leaves the value in LAST X unchanged In general LAST X in ALG mode is only useful in programs where it can often be used instead of a numbered storage register as it persists unchanged at least until digit entry or gF There is an example of its use in the Combinations program in the hp 12c platinum Solutio...

Page 245: ...theses Calculations In ALG mode parentheses can be used in calculations to change the order in which operations are evaluated When there are pending open parentheses the status indicator will be shown in the display As open parentheses are closed the expression contained within the parentheses is evaluated The final result of a calculation will be displayed when you press the key and then any pend...

Page 246: ...ow much money will you owe Keystrokes ALG mode Display OO 0 00 Clears any pending operations 1250 7b 87 50 Interest on the loan is 87 50 1 337 50 You owe this amount at the end of one year Percent Difference To find the percent difference between two numbers 1 Key in the base number 2 Press to separate the other number from the base number 3 Key in the other number 4 Press à Example Yesterday your...

Page 247: ... the first number 2 36 6 28 Adds the second number 1 67 7 95 Adds the third number to get the total 2 36 2 36 Keys in 2 36 to find out what percentage it is of the number in the display Z 29 69 Europe had nearly 30 of the total sales The Power Function Pressing q calculates a power of a number that is yx Like the arithmetic function q requires two numbers 1 Key in the base number which is designat...

Page 248: ...e described below Case 3 The calculator displays Error 3 This indicates that the computation is very complex possibly involving multiple answers and cannot be continued until you give the calculator an estimate of IRR The procedure for doing so is described below Case 4 The calculator displays Error 7 This indicates that there is no answer to the computation of IRR with the cash flow amounts you h...

Page 249: ...s by using the l function to help you make a good guess Remember that a correct IRR solution will make the calculated NPV very small So continue to guess interest rates and solve for NPV until the answer you obtain is reasonably close to zero Then press gt to calculate the IRR answer near your guess How would this work in case 2 above The calculator displays a negative answer and you wish to check...

Page 250: ... display the word Error followed by a digit 0 through 9 Listed below are operations that cannot be performed under the conditions specified The symbols x and y represent the number in the X and Y registers respectively when the operation key is pressed Error 0 Mathematics Operation Condition z x 0 y x 0 r x 0 x 0 q y 0 and x 0 y 0 and x is noninteger à y 0 Z y 0 z 0 through 4 x 0 e x is noninteger...

Page 251: ...istics Operation Condition Ö n number in R1 0 Σx 0 v n 0 n 1 nΣx2 Σx 2 0 nΣy2 Σy 2 0 R n 0 nΣx2 Σx 2 0 Q n 0 nΣy2 Σy 2 0 R Q nΣx2 Σx 2 nΣy2 Σy 2 0 Error 3 IRR Refer to Appendix C Error 4 Memory z Attempting to enter more than 400 program lines z Attempting to i to a program line that does not exist z Attempting storage register arithmetic in R5 through R9 or R 0 through R 9 z Too many open parenth...

Page 252: ... 0 and PMT 0 PMT is between FV d and PV d inclusive where d 100 1 100 S i i where S 0 for END mode and 1 for BEG mode i 100 n 0 n 1010 or n 0 i 100 Cash flows all have same sign i 100 P n 0 i 100 M i 100 x 0 x is noninteger l i 100 V Ý n 0 n 1010 x 0 x is noninteger E PMT 0 S PMT 0 ...

Page 253: ...e register specified does not exist or has been converted to program lines K a n specifies a storage register that does not exist or has been converted to program lines l L n 80 n 0 n is noninteger a x 99 x 0 x is noninteger Attempted to input Nj for CF0 Error 7 IRR Refer to Appendix C ...

Page 254: ... z You have reset the calculator using the reset hole see page 266 This is the case for the 31st of March May August October and December plus August 29 except in a leap year and 30 For example there is no September 31 so March 31 has no corresponding coupon date 6 months earlier To correct this problem for all maturity dates except August 29 and 30 add one day to both the settlement date and the ...

Page 255: ...nding periods i periodic interest rate expressed as a decimal PV present value FV future value or balance PMT periodic payment S payment mode factor 0 or 1 indicating treatment of PMT 0 corresponds to End 1 to Begin I interest amount INTG n integer portion of n FRAC n fractional portion of n Simple Interest i PV n I 360 360 i PV n I 365 365 ...

Page 256: ...PMT iS i PV Amortization n number of payment periods to be amortized INTj amount of PMT applied to interest in period j PRNj amount of PMT applied to principal in period j PVj present value balance of loan after payment in period j j period number INT1 0 if n 0 and payment mode is set to Begin PV0 i RND sign of PMT PRN1 PMT INT1 PV1 PV0 PRN1 INTj PVj 1 i RND sign of PMT for j 1 PRNj PMT INTj PVj P...

Page 257: ...RR CF j q j nq k j n j Calendar Actual Day Basis ΔDYS f DT2 f DT1 where f DT 365 yyyy 31 mm 1 dd INTG z 4 x and for mm 2 x 0 z yyyy 1 for mm 2 x INTG 0 4mm 2 3 z yyyy INTG Integer portion Note Additional tests are performed in order to ensure that the century but not millennium years are not considered leap years 30 360 Day Basis DAYS f DT2 f DT1 f DT 360 yyyy 30mm z for f DT1 if dd1 31 then z 30 ...

Page 258: ...ys in coupon period where settlement occurs DSC E DCS days from settlement date to next 6 month coupon date N number of semiannual coupons payable between settlement date and maturity date CPN annual coupon rate as a percentage YIELD annual yield as a percentage PRICE dollar price per 100 par value RDV redemption value For semiannual coupon with 6 months or less to maturity 2 2 100 2 100 CPN E DCS...

Page 259: ...le is less than z Call Value P N d1 Q N d2 Put Value Call Value Q P where d1 LN P Q v v 2 d2 d1 v Q Xe T r 1 0 0 v s 100 T Depreciation L asset s useful life expectancy SBV starting book value SAL salvage value FACT declining balance factor expressed as a percentage j period number DPNj depreciation expense during period j RDVj remaining depreciable value at end of period j RDVj 1 DPNj where RDV0 ...

Page 260: ...reciation 2 2 1 F W W SOYDk where W integer part of k F fractional part of k i e for k 12 25 years W 12 and F 0 25 Keyboard function 1 SAL SBV SOYD j L DPN L J Program for partial year 12 1 1 SAL SBV Y SOYD L DPN 2 1 SAL D SBV SOYD j LADJ DPN LADJ j for j 1 where 12 1 Y L LADJ Declining Balance Depreciation Keyboard function L FACT RBV DPN j j 100 1 for j 1 2 L Program for partial first year 12 10...

Page 261: ...esent value of the negative cash flows 1 100 1 n N P NPV NFV MIRR Advance Payments A number of payments made in advance A i i i FV PV PMT A n n 1 1 1 Interest Rate Conversions C number of compounding periods per year EFF the effective annual interest rate as a decimal NOM the nominal annual interest rate as a decimal Finite Compounding 1 1 C C NOM EFF Continuous Compounding 1 NOM e EFF ...

Page 262: ...Weighted Mean w wx xw Linear Estimation n number of data pairs Bx A y ˆ B A y x ˆ where n x x n y x xy B 2 2 x B y A n y y n x x n y x xy r 2 2 2 2 Standard Deviation 1 2 2 n n x x n sx 1 2 2 n n y y n sy Factorial 0 1 For n 1 where n is an integer n i i n 1 ...

Page 263: ... Cash Proceeds on Resale Market Value Mortgage Balance Commission The interest rate is obtained by solving the financial compound interest equation for i using n number of years house is owned PV down payment closing costs PMT mortgage payment taxes maintenance rent tax interest taxes FV net cash proceeds on resale Annual interest rate 12 i ...

Page 264: ...gins flashing replace the battery as soon as possible to avoid losing data Use only a fresh battery Do not use rechargeable batteries Warning There is the danger of explosion if the battery is incorrectly replaced Replace only with the same or equivalent type recommended by the manufacturer Dispose of used batteries according to the manufacturer s instructions Do not mutilate puncture or dispose o...

Page 265: ... steps 2 through 3 Make sure that the positive sign on each battery is facing outward 5 Replace the battery cover Note Be careful not to press any keys while the battery is out of the calculator If you do so the contents of Continuous Memory may be lost and keyboard control may be lost that is the calculator may not respond to keystrokes 6 Press to turn on the power If for any reason Continuous Me...

Page 266: ... is still no response the calculator requires service For a calculator that does respond to keystrokes 1 With the calculator off hold down the key and press 2 Release the key then release the key This initiates a complete test of the calculator s electronic circuitry If everything is working correctly within about 25 seconds during which the word running flashes the display should show 8 8 8 8 8 8...

Page 267: ...similar to that described above but continues indefinitely The test can be terminated by pressing any key which will halt the test within 25 seconds The z combination initiates a test of the keyboard and the display When the key is released certain segments in the display will be lit To run the test the keys are pressed in order from left to right along each row from the top row to the bottom row ...

Page 268: ...instructions after the date of purchase for the period specified above due to defects in material and workmanship when properly installed and used If HP receives notice of such defects during the warranty period HP will replace software media which does not execute its programming instructions due to such defects HP does not warrant that the operation of HP products will be uninterrupted or error ...

Page 269: ... products and services are set forth in the express warranty statements accompanying such products and services HP shall not be liable for technical or editorial errors or omissions contained herein FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND THE WARRANTY TERMS CONTAINED IN THIS STATEMENT EXCEPT TO THE EXTENT LAWFULLY PERMITTED DO NOT EXCLUDE RESTRICT OR MODIFY AND ARE IN ADDITION TO TH...

Page 270: ... 011 0524 Singapore 6100 6682 Czech Republic 296 335 612 South Africa 0800980410 Denmark 82 33 28 44 South Korea 2 561 2700 Ecuador 800 711 2884 Spain 913753382 El Salvador 800 6160 Sweden 08 5199 2065 Finland 09 8171 0281 Switzerland French 022 827 8780 France 01 4993 9006 Switzerland German 01 439 5358 Germany 069 9530 7103 Switzerland Italian 022 567 5308 Greece 210 969 6421 Taiwan 852 2805 256...

Page 271: ...Appendix F Battery Warranty and Service Information 271 Italy 02 754 19 782 Japan 81 3 6666 9925 Korea www hp com support korea Malaysia 65 6100 6682 ...

Page 272: ...ures z Reorient or relocate the receiving antenna z Increase the separation between the equipment and the receiver z Connect the equipment into an outlet on a circuit different from that to which the receiver is connected z Consult the dealer or an experienced radio or television technician for help Modifications The FCC requires the user to be notified that any changes or modifications made to th...

Page 273: ...e This product complies with the following EU Directives z Low Voltage Directive 2006 95 EC z EMC Directive 2004 108 EC Compliance with these directives implies conformity to applicable harmonized European standards European Norms which are listed on the EU Declaration of Conformity issued by Hewlett Packard for this product or product family This compliance is indicated by the following conformit...

Page 274: ...at it is recycled in a manner that protects human health and the environment For more information about where you can drop off your waste equipment for recycling please contact your local city office your household waste disposal service or the shop where you purchased the product Perchlorate Material special handling may apply This calculator s Memory Backup battery may contain perchlorate and ma...

Page 275: ...ractice differs significantly between the United Kingdom and the United States Mortgages The amount of the repayments on home loans and mortgages offered by banks in the United Kingdom can usually be calculated as described under Calculating the Payment Amount page 59 Building Societies in the United Kingdom however calculate the amount of these repayments differently In general the repayment amou...

Page 276: ...en rounding the result to one decimal place With the periodic interest rate in the display and in the i register and the payment mode set to End the effective annual rate can be calculated by pressing ÞP then keying in the number of compounding periods per year and pressing w0 M Pressing f1 will then display the rounded APR Bond Calculations Solutions for the price and yield to maturity of United ...

Page 277: ......

Page 278: ...ter to zero page 19 Arithmetic z Arithm etic operators page 21 Storage Registers Store Followed by number key decimal point and number key or top row financial key stores displayed number in storage register specified page 27 Also used to perform storage register arithmetic page 29 Recall Followed by number key decimal point and number key or top row financial key recalls value from storage regist...

Page 279: ...ction Key Index 279 two dates in the Y and X registers page 40 Financial CLEAR G Clears M Stores or computes future value final cash flow of a financial V Calculates depreciation using straight line method ...

Page 280: ...s stored with J K and a page 73 L Calculates the internal rate of return yield for up to 80 uneven cash flows and initial investment using values stored with J K and a page 78 J Initial cash flow Stores contents of displayed X register in R0 initializes n to zero sets N0 to 1 Used at the beginning of a discounted cash flow problem page 73 K Cash flow j Stores the contents of X register in Rj incre...

Page 281: ... square root of number in displayed X register page 100 q Raises number in Y register to power of number in X register page 102 y Computes reciprocal of number in displayed X register page 100 e Computes factorial n n 1 3 2 1 of number in displayed X register page 100 Natural antilogarithm Raises e approximately 2 718281828 to power of number in displayed X register page 100 Computes natural logar...

Page 282: ...e keycode keyboard row and location in row of the function key In Run mode function keys may be executed as part of a recorded program or individually by pressing from the keyboard Active Keys In Program mode only the following keys are active they cannot be recorded in program memory CLEARÎ Clear program Clears program memory to all i000 instructions and resets calculator so operations begin at l...

Page 283: ...executed page 127 Ç Single step Displays line number and keycode of current program memory line when pressed executes instruction displays result and moves to next line when released page 116 Ü Back step Displays line number and keycode of previous program memory line when pressed displays original contents of X register when released No instructions are executed page 118 Any key Pressing any key ...

Page 284: ...tus indicator 47 Black Scholes formula for valuing European options 194 254 Bonds 82 83 217 25 253 271 Bonds 30 360 day basis 217 21 Bonds annual coupon 222 Bonds corporate 82 Bonds municipal 82 Bonds U S Treasury 82 Branching 125 38 144 Branching adding instructions by 144 48 Branching conditional 129 30 Branching simple 125 C 74 76 73 74 76 79 17 21 42 73 230 19 35 230 234 236 C status indicator...

Page 285: ...ion declining balance 176 Depreciation excess 191 Depreciation partial year 171 91 Depreciation sum of the years digits 180 Depreciation with crossover 184 91 Digit entry recovering from errors in 92 Digit entry termination of 21 229 Discounted cashflow analysis 72 Display 87 Display format mantissa 89 Display format standard 88 Display formats number 87 Display scientific notation 88 Displaying n...

Page 286: ... indicator 16 M 37 1 13 Mantissa 18 89 Mantissa Display Format 89 Mean 94 Mean weighted 99 memory 27 Memory program 1 12 Modes alegebraic 20 RPN 20 Modified internal rate of return 192 Mortgage price of 159 Mortgage yield of 161 Multiple programs 149 N 41 49 100 231 75 79 80 72 73 Negative numbers 17 238 Net amount 33 Net present value 72 Net present value calculating 73 Nominal interest rate conv...

Page 287: ...06 153 Program running one line at a time 1 12 Program stopping 1 17 122 Program storing 149 Programming 104 Programs multiple 149 PV 45 R 42 69 230 106 1 17 122 17 21 27 41 108 230 19 42 88 100 231 Reciprocal 100 registers 27 Registers financial 41 Registers statistics 93 Renting versus Buying 163 Residual 209 Round 100 Rounding 87 RPN mode 20 23 228 Running message 13 78 S 96 230 84 230 84 230 1...

Page 288: ...288 Subject Index W Weighted mean 99 X 40 42 69 82 90 94 96 125 129 230 100 231 94 230 97 230 99 125 129 Y 13 82 83 97 230 102 231 230 Yield 206 212 ...

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