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Statistical Calculations 133

Conversions from Lower Tail

The distribution functions on the 10bII+ return values for the lower tail cumulative probability.

The lower tail probability corresponds to the area under the curve to the left of the given value.

Sometimes you will want to work with areas other than the lower tail. It is easy to convert from

lower tail to another area as long as you keep in mind that the total area under the curve is

equal to 1, and the Normal and the Student’s T distributions are symmetrical. In other words,

the portion of the curve to the left of zero is a mirror image of the portion of the curve to the

right of zero.

Example 1

The random variable Z is a standard normal random variable. What is the probability that

is greater than -1.7?

Figure 17

The probability that

is greater than -1.7 is the area of the curve to the right of -1.7. You can

calculate the area to the left of -1.7 and subtract it from 1 (total area of the curve).

Table 12-23 Example converting from lower tail

Keys

Display

Description

J7jy]F

.044565

Calculate the lower tail area.
Since the area is

1.7, change

the sign.

y1J4

.955435

Subtracts the lower tail from 1.

Summary of Contents for 10bII+

Page 1: ...i HP 10bII Financial Calculator User s Guide HP Part Number NW239 90001 Edition 1 May 2010 ...

Page 2: ...be liable for technical or editorial errors or omissions contained in the manual Hewlett Packard Company 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 exam ples contained herein Copyright 2010 Hewlett Packard Development Company L P Reproduction adaptation or translation of this manual is pro...

Page 3: ...iii HP 10bII Financial Calculator ...

Page 4: ...cent cash flow amount statistics entry backspace Swap percent change cash flow count delete statistics round Break even calculation 5 Change sign recall and memory Scientific notation store clear statistics parentheses Depreciation hyperbolic and trigonometric functions 6 Shift blue up Shift orange down 7 Numbered keys 1 and 4 9 Statistics weighted mean and estimation Statistical functions and reg...

Page 5: ...cal Calculations 17 Probability 19 Trigonometric Functions 20 2 Getting Started 23 Power On and Off 23 Manual Conventions and Examples 23 Basics of Key Functions 24 Shift Keys 25 Boxed Key Functions 25 Simple Arithmetic Calculations 26 Understanding the Display and Keyboard 29 Cursor 29 Clearing the Calculator 29 Annunciators 30 Input Key 32 Swap Key 32 Statistics Keys 32 Time Value of Money TVM C...

Page 6: ... Calculations 49 5 Picturing Financial Problems 55 How to approach a Financial Problem 55 Signs of Cash Flows 56 Periods and Cash Flows 56 Simple and Compound Interest 56 Interest Rates 57 Two Types of Financial Problems 58 Recognizing a Cash Flow Problem 59 6 Time Value of Money Calculations 61 Using the TVM Application 61 The TVM Keys 61 Begin and End Modes 62 Loan Calculations 62 Savings Calcul...

Page 7: ...05 Resetting the bond keys 108 11 Break even 109 The Break even Keys 109 Resetting the Break even keys 112 12 Statistical Calculations 113 Clearing Statistical Data 114 Entering Statistical Data 114 Viewing and Editing Statistical Data 116 Summary of Statistical Calculations 119 Mean Standard Deviations and Summation Statistics 120 Linear Regression Estimation and Regression Modes 121 Weighted Mea...

Page 8: ... IRR YR Calculations I Equations I 16 Appendix C Messages I 17 Warranty Regulatory and Contact Information 1 Replacing the Batteries 1 HP Limited Hardware Warranty and Customer Care 1 Limited Hardware Warranty Period 1 General Terms 2 Exclusions 2 Regulatory Information 3 Federal Communications Commission Notice 3 Modifications 3 Declaration of Conformity for Products Marked with FCC Logo United S...

Page 9: ...lay Description 0 00 Turns calculator on blue 0 00 Displays shift annunciator orange 0 00 Displays shift annunciator JGD 12_ Erases last character M 0 00 Clears display t 0 00 Clears statistics memory N 12 P_Yr message flashes then disappears Clears all memory Oj BOND CLR message flashes then disappears Clears bond memory OY BR EV CLR message flashes then disappears Clears break even memory OJ TVM...

Page 10: ...re 1 Figure 1 As an example the functions associated with the equals key 4 are illustrated in the text as follows primary function equals 4 secondary function display 5 tertiary function random 6 Boxed Key Functions These special functions require subsequent key presses to operate For example the functions associated with the clear key M include Table 1 2 Clearing functions Keys Associated Functio...

Page 11: ...ing price is 22 00 OY Clears break even memory OJ Clears TVM memory O Clears cash flow memory t Clears statistics memory Table 1 2 Clearing functions Keys Associated Function Table 1 3 Keys for percentage calculations Keys Description Percent Percent change À Cost Price Margin Ã Markup Table 1 4 Calculating the price Keys Display Description Jj7V 1 17 50 Enters number JV 4 20 13 Adds 15 ...

Page 12: ... Calculates price Table 1 7 Memory keys Keys Description ª Stores a constant operation s Stores a value in the M register memory location p Recalls a value from the M register m Adds a value to the number stored in the M register w When followed by a number key to d or 7 and to d stores a number in the display into a numbered data storage register There are 20 storage registers designated 0 19 Pre...

Page 13: ...t Keys Display Description JjPjª 7 00 Stores 7 as a constant operation 4 1 19 00 Multiplies 17 7 GG4 154 00 Multiplies 22 7 GV4 175 00 Multiplies 25 7 Table 1 9 Storing and recalling Keys Display Description VJd wG 519 00 Stores 519 in register 2 M 0 00 Clears display vG 519 00 Recalls register 2 Table 1 10 Storage register arithmetic Keys Display Description J7GV 1 25 Inputs 1 25 into the display...

Page 14: ...Description OJ Clears TVM memory and the current P_YR is displayed Ù Number of payments Ú Multiplies a value by the number of payments per year and stores as N Ò Interest per year Ï Present value Ì Payment É Future value Begin or End mode Í Number of payments per year mode Table 1 12 Calculating the monthly payment Keys Display Description OJ TVM CLR message flashes then disappears Clears TVM memo...

Page 15: ...122 86 Calculates payment if paid at end of period Table 1 12 Calculating the monthly payment Keys Display Description Table 1 13 Calculating a new payment Keys Display Description J yÌ 100 00 Enters new payment amount Money paid out is negative Ï 1 1 395 08 Calculates amount you can borrow Table 1 14 Calculating a new interest rate Keys Display Description d7VÒ 9 50 Enters new interest rate Ï 1 1...

Page 16: ...e loan Amortize the 1st through 24th loan payments Table 1 15 Amortizing the 20th payment of the loan Keys Display Description G Æ 20 00 Enters period to amortize Ê 20 20 Displays period to amortize 4 7 25 Displays principal 4 1 15 61 Displays interest Money paid out is negative 4 13 865 83 Displays the balance amount Table 1 16 Amortization example Keys Display Description JÆJG 12_ Enters range o...

Page 17: ... 13 836 22 Displays the balance amount Table 1 16 Amortization example Keys Display Description Table 1 17 Depreciation keys Keys Description Ù Expected useful life of the asset Ò Declining balance factor entered as a percentage Ï Depreciable cost of the asset at acquisition É Salvage value of the asset Straight line depreciation x Sum of the years digits depreciation u Declining Balance depreciat...

Page 18: ...itled Interest Rate Conversions in chapter 6 Time Value of Money Calculations 7 600 00 Remaining depreciable value after year one G 1 900 00 Depreciation of the asset in year two 5 700 00 Remaining depreciable value after year two Table 1 18 Calculating the depreciation Keys Display Description Table 1 19 Keys for interest rate conversion Keys Description Ó Nominal interest percent Ð Effective int...

Page 19: ...s up to 45 J identifies the cash flow number When preceded by a number pressing enters a cash flow amount number1 Ænumber 2 Enter a cash flow amount followed by Æ Enter a number for the cash flow count followed by to enter cash flow amount and count simultaneously v Opens editor for reviewing editing entered cash flows Press 1or Ato scroll through the cash flows Number of consecutive times cash fl...

Page 20: ...s initial outflow Yj 4 700 00 CF 1 flashes then disappears Enters first cash flow j ÆG 2 00 CFn 2 flashes then disappears Enters both the cash flow amount 7000 00 and count 2 00 simultaneously for second cash flow GD 23 000 00 CF 3 flashes then disappears Enters third cash flow v 0 40 000 00 Reviews entered cash flows starting with the initial cash flow Press 1 to scroll through the cash flow list...

Page 21: ... and calendar functions Keys Description È Enters dates in DD MMYYYY or MM DDYYYY formats D MY is the default Numbers at the far right of a calculated date indicate days of the week 1 is for Monday 7 is for Sunday Å Toggles between 360 and 365 day Actual calendars Ç Calculates the date and day past or future that is a given number of days from a given date Based on your current setting returned re...

Page 22: ...ess Èto select M DY format Table 1 26 Bond calculation keys Keys Description Oj Clears bond memory Û Calculates accrued interest only Ô Yield to maturity or yield to call date for given price Ñ Price per 100 00 face value for a given yield Î Coupon rate stored as an annual Ë Call value Default is set for a call price per 100 00 face value A bond at maturity has a call value of 100 of its face valu...

Page 23: ... Inputs the settlement date mm ddyyyy format S7 YG G 6 4 2020 4 Inputs the maturity date S7jV Î 6 75 Inputs CPN J Ë 100 00 Inputs call value Optional as default is 100 Y7jV Ô 4 75 Inputs Yield Ñ 1 15 89 Calculates the price 1 Û 2 69 Displays the current value for accrued interest 4 1 18 59 Returns the result for total price value of price value of accrued interest The net price you should pay for ...

Page 24: ... given profit or calculates it Stores the sales price per unit or calculates it Stores variable cost per unit for manufacturing or calculates it Stores the fixed cost to develop and market or calculates it Stores the expected profit or calculates it Table 1 29 Calculating break even Keys Display Description OY BR EV CLR message flashes then disappears Clears break even memory JV 150 000 00 Inputs ...

Page 25: ... statistical data x data Æy data Delete two variable statistical data v Opens editor for reviewing editing entered statistical data k Means of x and y T Mean of x weighted by y Also calculates b intercept h Sample standard deviations of x and y e Population standard deviations of x and y y data Z Estimate of x and correlation coefficient x data W Estimate of y and slope L Permits selection of six ...

Page 26: ...ription t 0 00 Clears statistics registers GÆV 1 00 Enters first x y pair YÆd 2 00 Enters second x y pair SÆJS 3 00 Enters third x y pair v 1 2 00 Reviews entered statistical data starting with the initial x value Press 1 to scroll through and verify the entered statistical data Press M to exit k 4 00 Displays mean of x 100 00 Displays mean of y h 2 00 Displays sample standard deviation of x 55 68...

Page 27: ...y I Calculates the cumulative Student s T probability given degrees of freedom and a T value o I Calculates a T value given degrees of freedom and the cumulative Student s T probability Calculates number of permutations of n items taken r at a time 9 Calculates number of combinations of n taken r at a time E Calculates factorial of n where 253 n 253 Table 1 33 Calculating the probability Keys Disp...

Page 28: ...o c R or C Calculates inverse sine inverse cosine and inverse tangent r c R or C Calculates hyperbolic sine cosine and tangent ro c R or C Calculates inverse hyperbolic sine cosine and tangent 3 Toggles between radians and degrees modes Degrees is the default setting Table 1 35 Trigonometry example Keys Display Description 7SG 62 Enters value of sine for oc 38 32 Calculates θ θ θ ...

Page 29: ...onvert the results to radians using Pi For more information on trigonometric functions refer to chapter 2 Getting Started Table 1 36 Converting to radians Keys Display Description P aJg 4 67 Converts degrees to radians ...

Page 30: ...At a Glance 22 ...

Page 31: ...ry or tertiary functions required for the problem For example the functions associ ated with the equals key 4 are illustrated in the text as follows primary function equals 4 secondary function display 5 tertiary function random 6 Note the symbol for the primary function of the key in this case appears on each of the key symbols depicted above This repetition is intended to serve as a visual aid B...

Page 32: ...ate the item after the is the default setting Except for the operating mode annunciators in the display indicate alternate settings are active M 0 00 Clears display t 0 00 Clears statistics memory N 12 P_Yr message flashes then disappears Clears all memory Oj BOND CLR message flashes then disappears Clears bond memory OY BR EV CLR message flashes then disappears Clears break even memory OJ TVM CLR...

Page 33: ... 2 to multiply a num ber in the display by itself To turn the shift annunciators off press or again Boxed Key Functions There are three shifted key functions on the calculator that are used to change the operation of another key s function These three tertiary functions O oand r are bound by blue boxes to show that they operate differently These special functions require subsequent key presses to ...

Page 34: ... than one operator consecutively for example 1 A 1 P 1 all are ignored except the last one If you make a typing mistake while entering a number press to erase the incorrect digits When a calculation has been completed by pressing 4 pressing a number key starts a new calculation OY Clears break even memory OJ Clears TVM memory O Clears cash flow memory Table 2 2 Clearing functions Keys Associated F...

Page 35: ...e currently displayed value You can do chain calculations without using 4 after each step Without clearing now calculate 4 9 3 In Chain mode if you wish to override the left to right order of entry use parentheses q and n to prioritize operations Table 2 5 Continuing a calculation Keys Display Description 1JJV7V4 356 42 Completes calculation of 240 92 1 15 5 Table 2 6 Chain calculations Keys Displ...

Page 36: ...12 pending operations An operation is pending when it is waiting for the input of a number or the result of an operation of higher priority Using Parentheses in Calculations Use parentheses to postpone calculating an intermediate result until you ve entered more numbers You can enter up to four open parentheses in each calculation For example suppose you want to calculate If you enter D agVA the c...

Page 37: ...e display and replaces it with 0 If entry is in progress pressing M clears the current entry and replaces it with 0 but the current calculation continues Otherwise M clears the display of its current contents and cancels the current calculation Clear Memory O followed by j Y J clears a selected memory type register Other memory is left intact P 0 41 Calculates 30 73 d4 3 70 Multiplies the result b...

Page 38: ...unciators Annunciators are symbols in the display that indicate the status of the calculator For functions that toggle between settings annunciators indicate alternate settings are active For the defaults no annunciators appear in the display For example when selecting a date format the default setting is month day year M DY When day month year D MY is active the D MY in the display indicates it i...

Page 39: ... an amortization is displayed CFLO The cash flow annunciator is lit together with one of the following two annunciators CF The cash flow number appears briefly then the cash flow is shown N The cash flow number appears briefly then the number of times the cash flow is repeated is shown STAT The statistics annunciator is lit together with one of the following two annunciators X The number of the da...

Page 40: ...in the mathematical stack This function is used to retrieve a secondary value returned during a calculation as well as to swap two items during a calculation Statistics Keys The statistics keys are used to access summary statistics from the statistics memory registers When you press followed by a statistics key you can recall one of six summary statistics with the next keystroke For example press ...

Page 41: ...o execute one number functions with a number displayed press the key or key combination corresponding to the operation you wish to execute The result is displayed See Table 2 14 for a list of one number functions Before doing any trigonometric calculations check whether the angle mode is set for degrees or radians Rad Degrees is the default setting The RAD annunciator in the display indicates radi...

Page 42: ... square of x K Calculates natural exponent to the power of x H Calculates natural log E Calculates factorial of n where 253 n 253 The Gamma function is used to calculate n for non integers or negative numbers c R or C Calculates sine cosine or tangent o c R or C Calculates inverse sine cosine or tangent r c R or C Calculates hyperbolic sine cosine or tangent ro c R or C Calculates inverse hyperbol...

Page 43: ...e display press 3 Table 2 15 Trigonometric functions Keys Description c Calculates sine written as sin R Calculates cosine written as cos C Calculates tangent written as tan oc Calculates inverse sine also written arcsin asin or sin 1 oR Calculates inverse cosine also written arccos acos or cos 1 oC Calculates inverse tangent also written arctan atan or tan 1 Table 2 16 Example using various trigo...

Page 44: ...at Table 2 16 Example using various trigonometric calculations Keys Display Description Table 2 17 Example using Pi Keys Display Description YP 3 14 Displays PY7V 2 20 25 Displays 4 52 4 254 47 Calculates sphere surface area in square centimeters π π π A 4πr 2 π Table 2 18 Hyperbolic and inverse hyperbolic functions Keys Description rc Calculates hyperbolic sine written as sinh rR Calculates hyper...

Page 45: ... in the first number followed by the function keys and then key in the second number followed by 4to return results Throughout the manual when examples are entered in this manner without using Æ they are referred to as in line functions For example the following keystrokes calculate the percent change between 17 and 29 using the keys as an in line function Table 2 19 Example performing various hyp...

Page 46: ...ters number 2 4 70 59 Calculates the percent change Table 2 21 Example calculating percent change using INPUT Keys Display Description JjÆ 17 00 Enters number1 and displays the INPUT annunciator indicating the number has been stored Gd 70 59 Enters number 2 and calculates the percent change Table 2 22 Example displaying two number functions with chain calculation Keys Display Description JjÆ 17 00...

Page 47: ...cription 1APa Addition subtraction multiplication division Q The power function Change 9 Combinations Permutations Ç The date and day past or future that is a given number of days from a given date Ä The number of days between two dates I Calculates the cumulative Student s t probability given degrees of freedom and a t value oI Calculates a t value given degrees of freedom and the cumulative Stud...

Page 48: ...ulates 1 12 4 52 88 Completes the calculation Table 2 25 Calculating the logarithm value Keys Display Description G7V K 12 18 Calculates e2 5 H 2 50 Calculates natural logarithm of the result jd 1Y E 24 00 Calculates 4 factorial 4 814 00 Completes calculation Table 2 26 Calculating the cube root Keys Display Description JGV QD4 1 953 125 00 Calculates 1253 JGV QD b4 5 00 Calculates the cube root o...

Page 49: ...for the first time numbers are displayed with two decimal places and a period as the decimal point The display format controls how many digits appear in the display If the result of a calculation is a number containing more significant digits than can be displayed in the current display format the number is rounded to fit the current display setting Table 2 27 Using last answer Keys Display Descri...

Page 50: ...ayed in DISP format it automatically displays in scientific notation Displaying the Full Precision of Numbers To set your calculator to display numbers as precisely as possible press 57 trailing zeros are not displayed To temporarily view all 12 digits of the number in the display regardless of the current display format setting press 5and hold 4 The number is displayed as long as you continue hol...

Page 51: ...0 with the decimal point moved 12 places to the left You can enter this number by pressing Y zyJG Interchanging the Period and Comma To switch between the period and comma United States and International display used as the decimal point and digit separator press 8 For example one million can be displayed as 1 000 000 00 or 1 000 000 00 Pressing 8 toggles between these options Rounding Numbers The...

Page 52: ...te list of error messages refer to Appendix C Table 2 31 Example displaying rounding off numbers Keys Display Description d7gjSVYD GJ 9 87654321_ Enters a number with more than two nonzero decimal places 5G 9 88 Displays two decimal places 54 while you press 4 987654321000 Displays all digits without the decimal 9 88 Rounds to two decimal places specified by pressing 5G 54 988000000000 Shows round...

Page 53: ... data You can use the 10bII to calculate simple percent percent change cost price margin and markup Percent key The key has two functions Finding a percent Adding or subtracting a percent Finding a Percent The key divides a number by 100 unless it is preceded by an addition or subtraction sign Example Find 25 of 200 Adding or Subtracting a Percent You can add or subtract a percent in one calculati...

Page 54: ...tracting a percent in a calculation Keys Display Description G A 200 00 Enters 200 GV 50 00 Multiplies 200 by 0 25 and subtracts 50 from 200 4 150 00 Completes the calculation Table 3 3 Adding a percent in a calculation Keys Display Description JGV 1j 4 1 337 50 Calculates loan interest 87 50 and adds 87 50 and 1250 00 to show the repayment amount Table 3 4 Calculating the percent change Keys Disp...

Page 55: ...s Example The standard markup on costume jewelry at Kleiner s Kosmetique is 60 They just received a shipment of chokers costing 19 00 each What is the retail price per choker Table 3 6 Keys for margin and markup Application Keys Description Margin À Margin is markup expressed as a percent of price Markup À Ã Markup calculations are expressed as a percent of cost Table 3 7 Calculating the margin Ke...

Page 56: ...utinely uses a 15 markup for what price should it sell a case of soup What is the margin 30 40 Calculates retail price Table 3 8 Calculating the retail price Keys Display Description Table 3 9 Calculating the margin Keys Display Description d7SÀ 9 60 Stores invoice cost JVÃ 15 00 Stores markup 1 1 04 Calculates the price on a case of soup 13 04 Calculates margin ...

Page 57: ...e recall and sum numbers with a single keystroke Use wand vto store to and recall from the 20 numbered registers Using Constants Use ª to store a number and arithmetic operator for repetitive calculations Once the constant operation is stored enter a number and press 4 The stored operation is performed on the number in the display Example 1 Calculate 5 2 6 2 and 7 2 Table 4 1 Storing 2 as constant...

Page 58: ... 23 and 43 Table 4 2 Storing 10 as a constant Keys Display Description J 1J ª 1 00 Stores 10 as a constant 4 1 1 00 Adds 10 to 10 4 12 10 Adds 10 to 1 1 GV4 27 50 Adds 10 to 25 Table 4 3 Storing y3 as a constant Keys Display Description G QDª 3 00 Stores y3 as constant 4 8 00 Calculates 23 Y4 64 00 Calculates 43 ...

Page 59: ...unnecessary to clear the M register since s replaces the previous contents However you can clear the M register by pressing s To add a series of numbers to the M register use sto store the first number and mto add subsequent numbers To subtract the displayed number from the number in the M register press y followed by m Table 4 4 Calculating percent change Keys Display Description VV DGª 32 00 Sto...

Page 60: ...re a number in the display into a numbered data storage register Press w7followed by through dto access registers 10 19 Press vfollowed by a number key to d or 7and to d to recall a number from a storage register Press v7followed by through dto access registers 10 19 Example In the following example two storage registers are used Set the calculator for CHAIN mode and calculate the following Table ...

Page 61: ...ou can do arithmetic inside storage registers R0 through R19 The result is stored in the register Table 4 7 Calculating the expression using two storage registers Keys Display Description YjV7S w7Y 475 60 Stores 475 60 displayed number in R14 aDd7JV wG 39 15 Stores 39 15 in R2 4 12 15 Completes first calculation VS 7J1 v7Y 1 035 70 Recalls R14 NOTE If the calculator is set for Algebraic mode press...

Page 62: ...n the storage register Keys Display Description YV7j wD 45 70 Stores 45 7 in R3 G7V wPD 2 50 Multiplies 45 7 in R3 by 2 5 and stores result 1 14 25 in R3 vD 1 14 25 Displays R3 Table 4 10 Storage register arithmetic Keys Display Description J7GV 1 25 Inputs 1 25 into the display w7V 1 25 Stores 1 25 in R15 D w17V 3 00 Adds 3 to 1 25 in R15 and stores the result R15 M 0 00 Clears the display v7V 4 ...

Page 63: ...cash flow diagram is the first step to solving a financial problem The following cash flow diagram represents investments in a mutual fund The original investment was 7 000 00 followed by investments of 5 000 00 and 6 000 00 at the end of the third and sixth months At the end of the 1 1th month 5 000 00 was withdrawn At the end of the 16th month 16 567 20 was withdrawn Figure 2 Cash flow diagram A...

Page 64: ...at either the beginning or end of a period If more than one cash flow occurs at the same place on the cash flow diagram they are added together or netted For example a negative cash flow of 250 00 and a positive cash flow of 750 00 occurring at the same time on the cash flow diagram are entered as a 500 00 cash flow 750 250 500 A valid financial transaction must have at least one positive and one ...

Page 65: ... 005 00 5 is 1 2 of 1 000 The second month the same process takes place on the new balance of 1 005 00 The amount of interest paid at the end of the second month is 1 2 of 1 005 00 or 5 03 The compounding process continues for the third fourth and fifth months The intermediate results in this illustration are rounded to dollars and cents Figure 3 Annual interest compounded monthly The word compoun...

Page 66: ...ed as simple interest calculations Financial problems are divided into two groups TVM problems Cash flow problems Recognizing a TVM Problem If uniform cash flows occur between the first and last periods on the cash flow diagram the financial problem is a TVM time value of money problem There are five main keys used to solve a TVM problem You can calculate any value after entering the other four va...

Page 67: ... deposit and a single withdrawal five years later Interest compounds monthly In this example PMT is zero Figure 5 Cash flow diagram Saving perspective Time value of money calculations are described in the next chapter titled Time Value of Money Calculations Recognizing a Cash Flow Problem A financial problem that does not have regular uniform payments sometimes called uneven cash flows is a cash f...

Page 68: ...n investment in a mutual fund This is an example of a problem that is solved using either Net Present Value or Á Internal Rate of Return per Year Figure 6 Cash flow diagram Investment in a mutual fund Cash flow problems are described in chapter 8 titled Cash Flow Calculations ...

Page 69: ...tering data for TVM calculations results are calculated based on data entered into specific memory registers When pressed the keys used for these operations store data enter known data for variables used during calculations calculate unknown variables based on stored data Table 6 1 Keys for performing TVM calculations Keys Stores or Calculates Ù Number of payments or compounding periods Ò Annual n...

Page 70: ... switch between modes press The BEGIN annunciator is displayed when your calculator is in Begin mode No annunciator is displayed when you are in End mode Mortgages and loans typically use End mode Leases and savings plans typically use Begin mode Loan Calculations Example A Car Loan You are financing a new car with a three year loan at 10 5 annual nominal interest compounded monthly The price of t...

Page 71: ...y 50 00 to 372 53 Table 6 2 Calculating the monthly payment Keys Display Description JG Í 12 00 Sets periods per year optional as 12 is the default DPJGÙ 36 00 Stores number of periods in loan J 7VÒ 10 50 Stores annual nominal interest rate JYV A JV Ï 13 000 00 Stores amount borrowed É 0 00 Stores the amount left to pay after 3 years Ì 422 53 Calculates the monthly payment The negative sign indica...

Page 72: ...ear mortgage what is the maximum purchase price you can afford Figure 8 Cash flow diagram Calculate PV Table 6 3 Calculating the interest rate Keys Display Description 1V Ì 372 53 Decreases payment from 422 53 Ò 2 03 Calculates annual interest rate for the reduced payment Table 6 4 Calculating the amount Keys Display Description J 7VÒ 10 50 Stores original interest rate DjVyÌ 375 00 Stores desired...

Page 73: ... 1 Calculate the loan payment using a 25 year term 2 Calculate the remaining balance after 4 years Step 1 First calculate the loan payment using a 25 year term Table 6 5 Calculating the maximum purchase price Keys Display Description JG Í 12 00 Sets periods per year D Ú 360 00 Stores the length of the mortgage 30 12 É 0 00 Pays mortgage off in 30 years j7VÒ 7 50 Stores interest rate dD yÌ 930 00 S...

Page 74: ...he balloon payment occur at the same time The final payment is the sum of PMT and FV Table 6 6 Calculating the monthly payment Keys Display Description JG Í 12 00 Sets periods per year GV Ú 300 00 Stores length of mortgage 25 12 300 months É 0 00 Stores loan balance after 25 years JjGV Ï 172 500 00 Stores original loan balance g7gÒ 8 80 Stores annual interest rate Ì 1 424 06 Calculates the monthly...

Page 75: ...e A Savings Account If you deposit 2 000 in a savings account that pays 7 2 annual interest compounded annually and make no other deposits to the account how long will it take for the account to grow to 3 000 Table 6 7 Calculating the final amount Keys Display Description Ì 1 424 06 Rounds payment to two decimal places then stores YgÙ 48 00 Stores four year term 12 4 that you expect to own house É...

Page 76: ... compounding to achieve a balance of at least 3 000 Calculate the actual balance at the end of six years Table 6 8 Calculating the number of years Keys Display Description OJ 0 00 Clears TVM memory J Í 1 00 Sets P YR to 1 since interest is compounded annually G yÏ 2 000 00 Stores amount paid out for the first deposit D É 3 000 00 Stores the amount you wish to accumulate j7GÒ 7 20 Stores annual int...

Page 77: ...h will be in the account on April 14 2010 Figure 12 Cash flow diagram Calculate FV Set to End mode Press if BEGIN annunciator is displayed Table 6 9 Calculating the balance after six years Keys Display Description SÙ 6 00 Sets n to 6 years É 3 035 28 Calculates the amount you can withdraw after six years Table 6 10 Calculating the balance amount Keys Display Description GY Í 24 00 Sets number of p...

Page 78: ...et to Begin mode Press if BEGIN annunciator is not displayed S7DÒ 6 30 Stores interest rate JV Ú 360 00 Stores the number of deposits É 52 975 60 Calculates the balance amount Table 6 1 1 Calculating the amount at the beginning of each month Keys Display Description JG Í 12 00 Sets payments per year Y yÏ 400 000 00 Stores your nest egg as an outgoing deposit jÒ 7 00 Stores annual interest rate you...

Page 79: ...ing the lease payment necessary to achieve a specified yield Finding the present value capitalized value of a lease The first payment on a lease usually occurs at the beginning of the first period Thus most lease calculations use Begin mode Example Calculating a Lease Payment A customer wishes to lease a 13 500 car for three years The lease includes an option to buy the car for 7 500 at the end of...

Page 80: ...s with monthly payments of 2 400 Payments are due at the beginning of the month with the first and last payments due at the onset of the lease You have an option to buy the forklift for 15 000 at the end of the leasing period If the annual interest rate is 9 what is the capitalized value of the lease Figure 15 Cash flow diagram Calculate PV of the lease Table 6 12 Calculating the monthly lease pay...

Page 81: ...ore the answer Step 3 Find the present value of the buy option Table 6 13 Calculating the present value Keys Display Description JG Í 12 00 Sets payments per year YjÙ 47 00 Stores number of payments GY yÌ 2 400 00 Stores monthly payment É 0 00 Stores FV for Step 1 dÒ 9 00 Stores interest rate Ï 95 477 55 Calculates the present value of 47 monthly payments Table 6 14 Adding the advance payment Keys...

Page 82: ...ess principal than payments near the end of a loan Figure 16 Graph Ì 0 00 Stores zero payment for this step of solution JV yÉ 15 000 00 Stores value to discount Ï 10 479 21 Calculates the present value of last cash flow Table 6 16 Calculating the present value of lease Keys Display Description 1p4 108 356 77 Calculates the present capitalized value of lease Rounding discrepancies are explained on ...

Page 83: ...ng and ending payments that will be amortized Press 4to see interest INT Press 4again to see the principal PRIN and again to see the balance BAL Continue pressing 4 to cycle through the same values again To amortize a range of payments enter starting period number Æending period number then press Ê The HP 10bII displays the annunciator PER followed by the starting and ending payments that will be ...

Page 84: ... store the other four values Next amortize the first year Table 6 18 Calculating the monthly payment Keys Display Description JG Í 12 00 Sets payments per year D Ú 360 00 Stores total number of payments j7jVÒ 7 75 Stores interest per year Jg Ï 180 000 00 Stores present value É 0 00 Stores future value Ì 1 289 54 Calculates the monthly payment Table 6 19 Calculating the loan balance after a year Ke...

Page 85: ...ucceeding years continue in the same fashion Example Amortizing a Single Payment Amortize the 1st 25th and 54th payments of a five year car lease The lease amount is 14 250 and the interest rate is 1 1 5 Payments are monthly and begin immediately Set to Begin mode Press if BEGIN annunciator is not displayed Table 6 20 Calculating the remaining balance Keys Display Description JDÆGY Ê 13 24 Display...

Page 86: ...Enters payment to amortize Ê 25 25 Displays PER and the amortized payment period 4 220 21 Displays PRIN and the principal paid on the 25th payment 4 90 21 Displays INT and the interest paid on the 25th payment 4 9 193 28 Displays BAL and the balance after the 25th payment VYÆ 54 00 Enters payment to amortize Ê 54 54 Displays PER and the amortized payment period 4 290 37 Displays PRIN and the princ...

Page 87: ...ominal rate by pressing Ó In the TVM application Ó and Ò share the same memory Interest conversions are used primarily for two types of problems Comparing investments with different compounding periods Solving TVM problems where the payment period and the interest period differ Investments With Different Compounding Periods Example Comparing Investments You are considering opening a savings accoun...

Page 88: ...t period complete the following steps 1 Enter the nominal rate and press Ó Enter the number of compounding periods in a year and press Í Solve for the effective rate by pressing Ð 2 Enter the number of payment periods in a year and press Í Solve for the adjusted nominal rate by pressing Ó Ð 6 87 Calculates the annual effective rate Table 6 24 Calculating the interest rate Second bank Keys Display ...

Page 89: ...ture value Set to Begin mode Press if BEGIN annunciator is not displayed Table 6 26 Calculating the equivalent nominal percentage rate Keys Display Description V Ó 5 00 Stores nominal percentage rate DSV Í 365 00 Stores bank s compounding periods per year Ð 5 13 Calculates annual effective rate JG Í 12 00 Stores monthly periods Ó 5 01 Calculates the equivalent nominal percentage rate for monthly c...

Page 90: ...Time Value of Money Calculations 82 Resetting the TVM Keys Press OJ to clear the TVM registers This sets N I YR PV PMT and FV to zero and briefly displays TVM CLR followed by the current value in P Yr ...

Page 91: ...epreciation also Ù The expected useful life of the asset in years Ï The depreciable cost of the asset at acquisition É The salvage value of the asset at the end of its useful life Straight line is a method of calculating depreciation presuming an asset loses a certain percentage of its value annually at an amount evenly distributed throughout its useful life x Sum of the years digits is an acceler...

Page 92: ...n using the declining balance method u and xeach place the amount of depreciation in the display and the TVM and X annunciators are displayed Press to display the remaining depreciable value the book value less the salvage value After pressing to display the remaining depreciable value note the X annunciator changes to Y Example 1 A metalworking machine purchased for 10 000 00 is to be depreciated...

Page 93: ...lue after year one X changes to Y in the display G 1 900 00 Enters the year for which depreciation is to be calculated and calculates the depreciation of the asset in year two 5 700 00 Displays remaining depreciable value after year two Table 7 2 Depreciation example using SL Keys Display Description Table 7 3 Depreciation example using SOYD Keys Display Description OJ TVM CLR message flashes then...

Page 94: ...ress O followed by J The messages TVM CLR and 12 P_yr appear briefly to indicate the TVM registers have been reset Keys Display Description OJ TVM CLR message flashes then disappears Clears TVM registers V Ï 5 000 00 Enters the depreciable cost of the asset at acquisition jÙ 7 00 Enters the expected useful life of the asset G Ò 200 00 Enters the double declining balance factor as a percentage É 0 ...

Page 95: ... enter the cash flow and a repeat value together enter the cash flow value followed by Æ then enter the repeat value followed by In general use the following steps for cash flow calculations on the HP 10bII 1 Organize your cash flows on paper A cash flow diagram is useful 2 Clear the cash flow memory 3 Enter the number of periods per year 4 Enter the amount of the initial investment CF0 using to e...

Page 96: ...annual cash flows P YR should be set to 1 for monthly cash flows use the default setting 12 number1 Cash flows up to 45 J identifies the cash flow number When preceded by a number pressing enters a cash flow amount number1 Æ number 2 Enter a cash flow amount followed by Æ Enter a number for the repeat value followed by This enters cash flow amount and repeat value simultaneously number 2 An altern...

Page 97: ... 35 data points clearing unneeded statistical information will free up more space for information When available memory is reached see Figure 3 the FULL annunciator indicates there is not enough space to continue saving data If you attempt to enter another cash flow at this point the ERROR annunciator is displayed In this case no additional cash flow data can be entered until some data in the stat...

Page 98: ...iagram Investments in stock Table 8 2 Example 1 a short term investment Keys Display Description O CFLO CLR message flashes then disappears Clears cash flow memory JG Í 12 00 Set payments per year V y 5 000 00 CF 0 flashes then disappears Enters initial cash flow Note the CFLO and CF annunciators G y 2 000 00 CF 1 flashes then disappears Enters first cash flow Note the CFLO and CF annunciators ...

Page 99: ...e that is required to give a net present value of zero The utility of these two financial tools becomes clear after working a few examples The next two sections describe organizing and entering your cash flows Examples of NPV NFV and IRR YR calculations follow Organizing Cash Flows The cash flow series is organized into an initial cash flow CF0 and succeeding cash flow groups up to 44 cash flows C...

Page 100: ...er year Table 8 3 Example calculating IRR and effective interest rate Keys Display Description O CFLO CLR message flashes then disappears Clears cash flow memory JG Í 12 00 Set payments per year JJ y 1 1 000 00 CF 0 flashes then disappears Enters initial cash flow Displays cash flow group number and amount Note the CFLO and CF annunciators 0 00 CF 1 flashes then disappears Enters first cash flow g...

Page 101: ...itor open press to return to CF0 To jump to a specific cash flow type the desired whole number of the desired cash flow item J and press The editor jumps to that position If the number is higher than your maximum current cash flow item count it will place you at the highest cash flow value If an invalid entry is typed such as a negative number or a non whole number the editor remains in its curren...

Page 102: ...otal number of cash flows press U 9 Press M to exit After completing the last example open the cash flow list and modify the following cash flows with the data in the table below Calculate the new IRR YR Table 8 4 Enter the new data Cash Flow Group New Cash Flow Amount New Cash Flow Count CF 0 1 1 000 00 1 CF 1 0 3 CF 2 1 000 00 2 CF 3 7 500 00 2 CF 4 1 200 00 2 Table 8 5 Editing cash flows Keys D...

Page 103: ...alculate NFV Example A Discounted Contract Uneven Cash flows You have an opportunity to purchase a contract with the following cash flows jV Æ1GÆ 3 2 00 Inputs new cash flow amount and repeat value Displays the new repeat value 2 00 for CF3 1JG yÆ1G Æ 4 is displayed first with no value followed by 4 1 200 then 4 2 00 Inputs new cash flow CF4 and repeat value X 3 600 00 Displays total of the cash f...

Page 104: ...follow Æwith the repeat value followed by even if the repeat value is 1 This process is shown here to demonstrate this application and for consistency with entering the data for the example Table 8 7 Entering uneven cash flows Keys Display Description O CFLO CLR message flashes then disappears Clear cash flow memory JG Í 12 00 Set payments per year ÆY 4 00 CFn 0 flashes then disappears Input initi...

Page 105: ...that this amount is positive The net present value is simply the summed or netted value of a series of cash flows when they are discounted to the front of the time line ÆY 4 00 CFn 4 flashes then disappears Input fifth cash flow amount and repeat value jV ÆJ 1 00 CFn 5 flashes then disappears Input sixth cash flow amount and repeat value Æd 9 00 CFn 6 flashes then disappears Input seventh cash flo...

Page 106: ...our convenience To recall that result press vÏ If you haven t changed the TVM values from the last example using NPV when you press vÏ the result is 27 199 92 When you calculate IRR YR the result is stored in I YR Press vÒto display the annualized yield More examples of NPV NFV and IRR YR calculations can be found in the chapter 13 titled Additional Examples ...

Page 107: ...onth year D MY formats In addition to a different display mode for the date and date calculations these functions also return different values based on the 365 day ACT and 360 day 360 calendars Press È to toggle between the formats The default setting is day month year dd mmyyyy Press Å to toggle between the 360 and 365 day actual calendars To specify the number of displayed decimal places 1 Press...

Page 108: ...o key in a date in D MY press È until the D MY annunciator appears 1 Key in one or two digits for the day 2 Press 7 3 Key in two digits for the month 4 Key in four digits for the year 5 Press either Ç or Ä to display the date in the selected number display format Using the INPUT key You can also enter dates for date calculations and the number of days using Æ To enter a date in M DY format using Æ...

Page 109: ...number of days 3 If the other date is in the past press y 4 Press Ç to display the date in the selected number display format Regardless of the setting for displayed places after the decimal point or whether you use Æor the in line feature the answer calculated by the Çfunction is displayed in a special format The numbers of the month day and year or day month and year are separated by digit separ...

Page 110: ...ne 4 2010 Assume the fiscal year ends on October 31st and you wish to calculate the actual number of days Actual using the D MY format Press Å if the 360 annunciator is displayed Calculate the example as an in line function Table 9 2 Date calculation example as an in line function Keys Display Description JG7JgG JJ 12 18201 1_ Keys in the date in MM DDYYYY format ÇJ 4 3 27 2012 2 Calculates the da...

Page 111: ...s the desired calendar format in this case actual days optional if the 360 annunciator is not displayed as Actual is the default 5S 0 000000 Sets the number of displayed decimal places so the entire date is displayed optional Y7 SG J Ä 4 062010 Inputs the starting date in the selected format DJ7J G J 4 149 000000 Inputs the ending date in the selected format and calculates the number of actual day...

Page 112: ...able 9 6 Calculating the actual number of days using the INPUT key Keys Display Description M 0 00 Clear display J 7JjG JGÆ 10 17 Keys in the date in MM DDYYYY format and displays digits in the selected display format 2 S7 YG JV Ä 960 00 Returns the same results ...

Page 113: ...memory Û Calculates accrued interest only Ô Yield to maturity or yield to call date for given price Ñ Price per 100 00 face value for a given yield Î Coupon rate stored as an annual Ë Call value Default is set for a call price per 100 00 face value A bond at maturity has a call value of 100 of its face value È Date format Toggle between day month year dd mmyyyy or month day year mm ddyyyy Å Day co...

Page 114: ...nd Date Calculations The range of acceptable dates is October 15 1582 to December 31 9999 Verify that bond day counts 360 365 and annual or semiannual coupon payment schedules are appropriate for your problem prior to inputting your data Example 1 What price should you pay on April 28 2010 for a 6 75 U S Treasury bond maturing on June 4 2020 if you want a yield of 4 75 Assume the bond is calculate...

Page 115: ... Optional as default is 100 Note if Call requires another value key in the number followed by Ë Y7jV Ô 4 75 Inputs 4 75 for Yield Ñ 1 15 89 Calculates the price 1 Û 2 69 Displays the current value for accrued interest 4 1 18 58 Returns the result for total price value of price value of accrued interest The net price you should pay for the bond is 1 18 58 Table 10 2 Bond calculation example Keys Di...

Page 116: ...ond registers have been reset To return to the default calculator screen press M J 7JVG G 10 15 2020 4 Inputs October 15 2020 for the maturity date Y7JVG JG 4 15 2012 7 Inputs April 15 2012 for the settlement date Ô 5 72 Calculates yield as a Table 10 4 Keys Display Description J Ë 100 00 Inputs new call value Since the bond will not be called the bond at maturity has a call value of 100 of its fa...

Page 117: ... The Break even Keys When entering data for break even calculations results are calculated based on data entered into specific memory registers When pressed the keys used for these operations store data enter known data for variables used during calculations calculate unknown variables based on stored data Table 1 1 1 Break even keys Key Description OY Clears break even memory Stores the quantity ...

Page 118: ... sold to make a profit of 10 000 00 Table 1 1 2 Break even example Keys Display Description OY BK EV CLR message flashes then disappears Clears break even memory JV 150 000 00 Inputs fixed cost GV 250 00 Inputs variable cost per unit D 300 00 Inputs price J 10 000 00 Inputs profit 3 200 00 Calculates the current value for the unknown item UNITS ...

Page 119: ...the purpose of the example will be 0 00 Table 1 1 3 Calculating the projected maximum fixed cost Keys Display Description OY BK EV CLR message flashes then disappears Clears break even memory J 10 000 00 Inputs the projected number of units YV 45 00 Inputs the projected selling price GD 23 00 Inputs the variable cost per unit 0 00 Inputs the profit in this case 0 220 000 00 Calculates the maximum ...

Page 120: ...g the Break even keys To reset the break even keys to their default values press OY A brief message flashes on the screen to indicate the break even registers have been reset To return to the default calculator screen press M ...

Page 121: ...cs memory x value Enter one variable statistical data x value Delete one variable statistical data x valueÆ y value Enter two variable statistical data x value Æ y value Delete two variable statistical data v Opens editor for reviewing or editing statistical data k Means of x and y T Mean of x weighted by y Also calculates b coefficient h Sample standard deviations of x and y e Population standard...

Page 122: ...ional data points may be stored in memory shared with the cash flow memory See Figure 1 Figure 1 As illustrated in Figure 1 if no more than 15 cash flows are stored in the cash flow memory you may store up to 45 data points for statistical usage If more than 15 cash flows are stored in the cash flow memory the total memory available for storing statistical data is reduced For example in Figure 2 t...

Page 123: ... HP 10bII displays n the number of items accumulated 3 Continue accumulating values by entering the numbers and pressing The n value is increased with each entry Two Variable Statistics and Weighted Mean To enter x y pairs of statistical data complete these steps 1 Clear the statistical registers by pressing t 2 Enter the first x value and press Æ The HP 10bII displays the x value 3 Enter the corr...

Page 124: ...tered number is higher than your maximum data pair in which case it will jump to the highest x value If you type in an invalid number such as a negative number or a non whole number the editor remains in its current position 5 To delete the currently displayed statistical data pair press a To add a new pair with the x and y values equal to zero press P 6 To replace the currently displayed value si...

Page 125: ...scription t STAT CLR message flashes briefly then disappears Clears the statistics memory DGÆYJV 1 00 Enters first ordered pair DVÆVJV 2 00 Enters the second ordered pair DgÆjGV 3 00 Enters the third ordered pair v 1 32 00 Open the editor Displays X annunciator 11111 3 725 00 Scroll and verify the data points starting with the x value of the first pair The y value of the third pair is displayed M ...

Page 126: ...rth ordered pair DjÆSgV 5 00 Enters fifth ordered pair Table 12 5 A new prediction Keys Display Description YV W 1 204 67 Predicts the drinks sold at 45oC But is this the best fit L 0 00 Sets regression mode to 0 BEST FIT YV W 1 128 12 All regressions are calculated and LINEAR is selected as being a better fit than POWER The result 1 128 is well within the limit of six employees ...

Page 127: ...et of data The population standard deviation assumes that the data constitutes the entire population e Population standard deviation of the x values NOTE The sample standard deviation assumes that the data is a sampling of a larger complete set of data The population standard deviation assumes that the data constitutes the entire population Population standard deviation of the y values if you ente...

Page 128: ... carry out the sail change and records the numbers of minutes required 4 5 4 2 3 25 3 5 3 75 Calculate the mean and sample standard deviation of the times Also calculate the root mean square using the formula Table 12 7 Example calculating mean standard deviation and summation statistics Keys Display Description t STAT CLR message flashes briefly then disappears Clears statistics memory Y7V 1 00 E...

Page 129: ...cal method for estimation and forecasting It is used to find a straight line that best fits a set of x y data There must be at least two different x y pairs The straight line provides a relationship between the x and y variables y mx b where m is the slope and b is the y intercept Table 12 8 Example 3 Keys Display Description t STAT CLR message flashes briefly then disappears Clears statistics mem...

Page 130: ...straight line calculated by linear regression can be used to estimate a y value for a given x value or vice versa 1 Enter the x y data 2 Enter the known x value or y value To estimate x for the given y enter the y value then press Z To estimate y for the given x enter the x value then press W Example 4 Ali s Azaleas advertises on a local radio station For the past six weeks the manager has kept re...

Page 131: ...le 12 10 Example for forecasting Keys Display Description t STAT CLR message flashes briefly then disappears Clears statistics memory GÆJY 1 00 Enters minutes and sales for consecutive weeks JÆdG 2 00 DÆJJ 3 00 VÆGGSV 4 00 VÆGgd 5 00 YÆGG 6 00 T 376 25 Calculates y intercept W 425 88 Displays slope ...

Page 132: ... survey of 266 one bedroom rental apartments reveals that 54 of them rent for 500 per month 32 for 505 88 for 510 and 92 for 516 What is the average monthly rent Z 0 90 Calculates correlation coefficient Table 12 1 1 Estimating the level of sales Keys Display Description j W 3 357 38 Estimates sales if 7 minutes of advertising were purchased g W 3 783 25 Estimates sales if 8 minutes were purchased...

Page 133: ...M As an alternative to scrolling and if you know the number of the desired model press L followed by the desired number of the fit option Table 12 13 Calculating the average monthly rent Keys Display Description t STAT CLR message flashes briefly then disappears Clears statistics memory V ÆVY 1 00 Enters first rent and its weight V VÆDG 2 00 Enters second rent and its weight VJ Ægg 3 00 Enters thi...

Page 134: ...in operations that allow this are Factorial Factorial is a mathematical operator that instructs you to multiply the current number by all previous whole numbers Writing out so many numbers can be cumbersome so mathematicians use to signify this process For example 5 is equivalent to 5 x 4 x 3 x 2 x 1 120 On the 10bII the input value n must be within 253 n 253 The gamma function is used to calculat...

Page 135: ...ample Using five colored balls how many different color combinations of three colors can be chosen Random Number and Seed The 10bII includes a random number generator function that generates a pseudo random number in the range 0 x 1 To store a seed value type a positive number and press w 6 Storing a value of 0 will select a random number and store it as the seed value Keys Display Description V D...

Page 136: ... functions replace the statistical tables found in the back of textbooks Unlike the textbook the calculator can calculate any value not just a limited selection found in the table Table 12 17 Example storing a seed value and generating random numbers Keys Display Description YG w 6 42 00 Stores 42 as the random number generator seed 5d 42 000000000 Set display precision 6 199873749 Generate first ...

Page 137: ...ess F This function calculates the probability that a standard normal random variable Z is less than z Figure 5 Example The variable Z is a standard normal random variable What is the probability that Z is less than 1 7 Table 12 19 Probability example Keys Display Description 5S 000000 Set display precision J7jy F 044565 Calculate the probability Figure 6 Figure 7 ...

Page 138: ... Tail Probability Figure 8 What is the z value corresponding to a lower tail cumulative probability of 025 Table 12 20 Example calculating z value lower tail Keys Display Description 7 GV oF 1 959964 Calculate the corresponding z value Figure 9 Figure 10 ...

Page 139: ...umber function so it may be entered as either an in line function or by using Æ Example What is the lower tail probability associated with a Student s T distribution with 8 degrees of freedom df1 with a t value of 1 86 Table 12 21 Example of Student s t lower tail Keys Display Description g IJ7gSy4 0499653 Calculates the lower tail probability or using Æ gÆJ7gSy I Returns the same results Figure 1...

Page 140: ...igure 14 Example A hypothesis test requires a critical t value from the Student s T distribution with 26 degrees of freedom Find the t value for a lower tail probability of 05 Table 12 22 Example calculating the t value lower tail Keys Display Description GS oI7 V4 1 705618 Enter degrees of freedom and the probability and calculates the lower tail t value or using Æ GSÆ7 V oI Returns the same resu...

Page 141: ...Student s T distributions are symmetrical In other words the portion of the curve to the left of zero is a mirror image of the portion of the curve to the right of zero Example 1 The random variable Z is a standard normal random variable What is the probability that z is greater than 1 7 Figure 17 The probability that z is greater than 1 7 is the area of the curve to the right of 1 7 You can calcu...

Page 142: ...18 The desired area is to the right of 1 2 and to the left of 1 2 Since normal distributions are symmetrical and the areas are the same you can calculate the lower tail area and simply multiply by 2 Table 12 24 Example converting from lower tail Keys Display Description J7Gy F 1 15070 Calculate the lower tail area and store the value PG4 230139 Calculates the result ...

Page 143: ...o 0 95 Figure 19 The given area is 0 95 The area not included is 1 0 95 2 0 025 Since the normal distribution is symmetrical half of the desired area is in the lower tail 05 2 025 The desired area corresponds to a lower tail probability of 025 Table 12 25 Example converting from lower tail the inner area Keys Display Description 7 GV oF 1 959964 Returns desired value of z ...

Page 144: ...Statistical Calculations 136 ...

Page 145: ...s your cost is 40 000 You want a 20 rate of return What price should you charge per unit Forecasting Based on History One method of forecasting sales manufacturing rates or expenses is reviewing historical trends Once you have historical data the data are fit to a curve that has time on the x axis and quantity on the y axis Example Given the following sales data what are the sales estimates for ye...

Page 146: ...yment DISC is the discount percent if the payment is made early TOTAL DAYS is the total number of days until the bill must be paid DISC DAYS is the number of days for which the discount is available Example You receive a bill with the credit terms 2 10 NET 30 What is the cost of not taking the cash discount Table 13 3 Calculating the sales estimates for years six and seven Keys Display Description...

Page 147: ... Continuous Compounding The equation for calculating an effective rate for continuous compounding is Table 13 4 Calculating the cost without the cash discount Keys Display Description GPDS PJ a 72 000 00 Calculates numerator in equation q qJ AG n 98 00 Parentheses force order of calculation P qD A J 4 36 73 Calculates as an annual percentage rate cost of not taking discount Table 13 5 Calculating ...

Page 148: ...sit 250 00 in the account What will the balance be after 15 years Set to End Mode Press if BEGIN annunciator is displayed Table 13 6 Calculating the annual nominal rate Keys Display Description Jg 0 18 Divides nominal rate by 100 K 1 20 Raises e to 0 18 power AJPJ 4 19 72 Calculates annual effective rate Ð 19 72 Stores effective rate JG Í 12 00 Sets payments per year Ó 18 14 Calculates the annual ...

Page 149: ...in full a balloon payment at the end of its fifth year What is the yield to the purchaser if the price of the mortgage is 79 000 Step 1 Calculate PMT Make sure FV 0 Set to End Mode Press if BEGIN annunciator is displayed Step 2 Enter the new value for N indicating when the balloon occurs then find FV the amount of the balloon É Table 13 8 Calculating the monthly payment Keys Display Description JG...

Page 150: ... Example APR for a Loan With Fees A borrower is charged two points for the issuance of a mortgage One point is equal to 1 of the mortgage amount If the mortgage amount is 160 000 for 30 years and the annual interest rate is 8 5 with monthly payments what APR is the borrower paying Set to End Mode Press if BEGIN annunciator is displayed V Ú 60 00 Stores number of payments until balloon É 88 706 74 ...

Page 151: ...tes payment vÏ 160 000 00 Recalls loan amount AG Ï 156 800 Subtracts points Ò 8 72 Calculates APR considering fees Table 13 12 Calculating the annual percentage rate Keys Display Description JG Í 12 00 Sets payments per year JGÒ 12 00 Stores interest rate J Ú 120 00 Stores length of mortgage J Ï 1 000 000 00 Stores original amount of mortgage yÉ 1 000 000 00 Enters amount due at end of term Paymen...

Page 152: ...be 0 5 periods assuming a whole period to be a 30 day month 2 Calculate the payment using the new PV with N equal to the number of full periods Use Begin mode if the number of days until the first payment is less than 30 otherwise use End mode Example A 36 month loan for 4 500 has an annual rate of 15 If the first monthly payment is made in 46 days what is the monthly payment amount assuming 30 da...

Page 153: ...e the first option Calculate the second option É 0 00 Enters amount left to pay after 36 payments Ì 157 03 Calculates the payment amount Table 13 13 Calculating the monthly payment amount Keys Display Description Table 13 14 Calculating the annual interest rate of 3 5 Keys Display Description JG Í 12 00 Sets payments per year DSÙ 36 00 Stores known values JGV Ï 12 500 00 Stores loan amount É 0 00 ...

Page 154: ...rtize a 30 year 130 000 Canadian mortgage if the annual interest rate is 12 d7VÒ 9 50 Stores second interest rate Ì 368 38 Calculates payment PvÙ4 13 261 64 Calculates total interest and principal Table 13 15 Calculating the annual interest rate of 9 5 Keys Display Description Table 13 16 Calculating the monthly payment for Canadian mortgage Keys Display Description JG Ó 12 00 Stores known nominal...

Page 155: ...tted line for a 30 year 735 000 mortgage on a vacation home The annual interest rate is 1 1 2 Part 1 What will your payments be at the end of the month Set to End mode Press if BEGIN annunciator is displayed Part 2 Your company s regular payroll is generated every other Friday The bank agrees to automatically draw payments of 3 555 00 out of each paycheck approximately half of what a monthly payme...

Page 156: ...est compounded monthly and you plan to make monthly deposits starting at the end of the current month The deposits cease when she begins college How much do you need to deposit each month This problem is solved in two steps First calculate the amount you ll need when she starts college Start with an interest rate conversion because of the monthly compounding GS Í 26 00 Sets payments per year for e...

Page 157: ...isplay Description d Ó 9 00 Stores annual nominal rate JG Í 12 00 Stores number of compounding periods used with this nominal rate Ð 9 38 Calculates annual effective rate Ò 9 38 Stores effective rate as annual rate Table 13 21 Calculating the amount required at the start Keys Display Description J Í 1 00 Sets 1 payment per year JV Ì 15 000 00 Stores annual withdrawal YÙ 4 00 Stores number of withd...

Page 158: ...on the inflation rate and the duration of the account Example You are considering opening a tax deferred account with a dividend rate of 8 175 If you invest 2 000 at the beginning of each year for 35 years how much will be in the account at retirement How much will you have paid into the account How much interest will you have earned If your post retirement tax rate is 15 what will the after tax f...

Page 159: ... deposits have been taxed already Table 13 23 Calculating the purchasing power of the amount Keys Display Description J Í 1 00 Sets 1 payment per year DVÙ 35 00 Stores number of periods and interest rate g7JjVÒ 8 18 Ï 0 00 Stores amount you start with G yÌ 2 000 00 Stores amount of annual payment É 387 640 45 Calculates amount in account at retirement vÌPvÙ4 70 000 00 Calculates amount you have pa...

Page 160: ...cash flow applications Example You have 82 monthly payments of 754 left on your 8 mortgage leaving a remaining balance of 47 510 22 You would like to wrap that mortgage and borrow an additional 35 000 for another investment You find a lender who is willing to wrap an 82 510 22 mortgage at 9 5 for 15 years What are your new payments and what return is the lender getting on this wrap around mortgage...

Page 161: ...of view Figure 22 Cash flow diagram Wrap around mortgage When you group the above cash flows you ll find that CF0 47 510 22 82 510 22 35 000 CF1 861 59 754 00 107 59 Table 13 25 Calculating the payment Keys Display Description OJ 0 00 Clears TVM registers JG Í 12 00 Sets payments per year gGVJ 7GG Ï 82 510 22 Stores loan amount on which your new payment is calculated d7VÒ 9 50 Stores interest rate...

Page 162: ...o years into a money market fund earning 8 8 What is the current balance of the account Figure 23 Cash flow diagram Table 13 26 Calculating the annual return Keys Display Description DV y CF0 35 000 00 Enters 35 000 for loan amount vÌyAjVY CF1 107 59 Enters net payment for first 82 months gG n1 82 00 Enters number of times payment occurs vÌy CF2 861 59 Enters net payment for next 98 months Jg AgG ...

Page 163: ...se of used batteries according to the manufacturer s instructions The calculator is powered by two 3 volt CR2032 coin batteries When changing batteries use only fresh coin cell batteries Do not use rechargeable batteries Do not mutilate puncture or dispose of batteries in fire The batteries can burst or explode releasing hazardous chemicals Do not use new and old batteries together and do not mix ...

Page 164: ...Erase the memory see below The All Clear message should now be displayed If this is not the case the calculator requires service Resetting the calculator 1 Turn the calculator over and remove the battery cover 2 Insert the end of a paper clip into the small round hole located between the batteries Insert the clip gently as far as it will go Hold for one second and then remove the clip 3 Press 4 If...

Page 165: ...tact us using the contact information and phone numbers listed on the product CD Q I m not sure if the calculator is malfunctioning or if I m doing something incorrectly How can I determine if the calculator is operating properly A See Determining If the Calculator Requires Service Q My numbers contain commas instead of periods as decimal points How do I restore the periods A Press 8 Ch 2 Getting ...

Page 166: ...NPUT in the display mean A The Æ key has been pressed Ch 2 Getting Started Q Why is IRR YR larger than I expected A This is IRR per year To see a periodic IRR divide IRR YR by P YR Environmental Limits To maintain product reliability you should avoid getting the calculator wet and observe the following temperature and humidity limits Operating temperature 0 to 40 C 32 to 104 F Storage temperature ...

Page 167: ... only positive answer However one or more negative answers may exist Case 2 The calculator displays a negative answer and no message This is the only answer Case 3 The calculator displays No Solution There is no answer This situation might be the result of an error such as a mistake in keying in the cash flows A common mistake that results in this message is putting the wrong sign on a cash flow A...

Page 168: ...splay setting For each payment amortized Interest Rate Conversions i I YR P YR 0 PV 1 i S 100 PMT 1 1 i 100 N i 100 FV 1 i 100 N ΣINT accumulated interest ΣPRN accumulated principal i periodic interest rate INT BAL i INT is rounded to the current display setting INT 0 for period 0 in Begin mode INT INT with sign of PMT PRN PMT INT BALnew BALold PRN ΣINTnew ΣINTold INT ΣPRNnew ΣPRNold PRN i I YR P ...

Page 169: ...re N TOTAL COUNT i periodic interest rate j the group number of the cash flow CFj amount of the cash flow for group j nj number of times the cash flow occurs for group j k the group number of the last group of cash flows Nj total number of cash flows prior to group j nl 1 l j NPV CF0 CFj j 1 k 1 1 i 100 nj i 100 1 i 100 nj nj j 1 k nj CFj j 0 k nj j 0 k ...

Page 170: ...umber Y annual yield as a decimal fraction YLD 100 For one or fewer coupon period to redemption Note coupon CPN is a percentage CPN in both cases For more than one coupon period to redemption The end of month convention is used to determine coupon dates in the following exceptional situations This affects calculations for YLD PRICE and ACCRU If the maturity date falls on the last day of the month ...

Page 171: ...reciation DB equals the remaining depreciable value for the prior year Statistics SL BASIS SALV LIFE SOYD BASIS SALV LIFE LIFE 1 2 LIFE YR 1 DB BASIS FACT 100 LIFE 1 FACT 100 LIFE YR 1 x x n y y n xw xy y Sx x 2 x 2 n n 1 Sy y 2 y 2 n n 1 σx x 2 x 2 n n σy y 2 y 2 n n r xy x y n x 2 x 2 n y 2 y 2 n m xy x y n x 2 x 2 n b y mx x y b m y mx b ...

Page 172: ...Appendix B More About Calculations VI Forecasting Name Fit Best Fit Automatically selects fit Linear m x b Logarithm m ln x b Exponential b e m x Power b xm Exponent b mx Inverse m x b ...

Page 173: ... for values entered Appendix B not Found A solution for IRR YR or I YR may or may not exist If you are attempting to solve I YR you may be able to perform the calculation using IRR YR If you are attempting an IRR YR calculation refer to Appendix B Error I_Yr Invalid value in I Yr register or error solving for I Yr Error P_Yr Invalid value in P Yr register or error solving for P Yr Error N Invalid ...

Page 174: ...re cleared Best Fit The calculator selected the best fit regression which is subsequently flashed for 1 second running Displays if a calculation takes longer than 25 seconds User Stop An IRR YR I YR or amortization calculation was interrupted by pressing M Table C 1 Messages Message Displayed Description ...

Page 175: ...lator is off When changing the batteries change the batteries one at a time to avoid clearing the memory As a back up write down any data that you have stored and might need for later use 3 Turn the calculator over and pry off the battery cover 4 Gently remove one battery 5 Insert the new battery making sure that the positive sign battery is facing outward 6 Gently remove the other battery 7 Inser...

Page 176: ...ORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU Notwithstanding the above disclaimers HP expressly warrants to you the end user customer that HP hardware accessories and supplies will be free from defects in materials and workmanship after the date of purchase for the period specified above If HP receives notice of such defects during the warranty period HP will at its option ei...

Page 177: ... AND NEW ZEALAND THE WAR RANTY TERMS CONTAINED IN THIS STATEMENT EXCEPT TO THE EXTENT LAWFULLY PERMITTED DO NOT EXCLUDE RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU Regulatory Information Federal Communications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device p...

Page 178: ... Class B digital apparatus meets all requirements of the Canadian Interference Causing Equipment Regulations Avis Canadien Cet appareil numérique de la classe B respecte toutes les exigences du Règlement sur le matériel brouilleur du Canada European Union Regulatory Notice Products bearing the CE marking comply with the following EU Directives Low Voltage Directive 2006 95 EC EMC Directive 2004 10...

Page 179: ...signated collection point for the recycling of waste electrical and electronic equipment The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that 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 con...

Page 180: ...tes may apply A complete list is available on the web at www hp com support Contact Information Table 17 1 Contact Information Country Region Contact Country Region Contact Algeria www hp com support Anguila 1 800 71 1 2884 Antigua 1 800 71 1 2884 Argentina 0 800 555 5000 Aruba 800 8000 800 71 1 2884 Austria Österreich 01 360 277 1203 Bahamas 1 800 71 1 2884 Barbados 1 800 71 1 2884 Belgique Franç...

Page 181: ...ary www hp com support India 1 800 1 14772 Indonesia 21 350 3408 Ireland 01 605 0356 Italy Italia 02 754 19 782 Jamaica 1 800 71 1 2884 Japan 日本 00531 86 001 1 Kazakhstan www hp com support Latvia www hp com support Lebanon www hp com support Lithuania www hp com support Luxembourg 2730 2146 Malaysia 1800 88 8588 Martinica 0 800 990 01 1 877 219 8671 Mauritius www hp com support Mexico México 01 8...

Page 182: ...nt 01 800 71 1 2884 Suriname 156 800 71 1 2884 Swaziland www hp com support Sweden Sverige 08 5199 2065 Switzerland 022 827 8780 Switzerland Suisse Français 022 827 8780 Switzerland Schweiz Deutsch 01 439 5358 Switzerland Svizzeera Italiano 022 567 5308 Taiwan 臺灣 00801 86 1047 Thailand ไทย 2 353 9000 Trinidad Tobago 1 800 71 1 2884 Tunisia www hp com support Turkey Türkiye www hp com support Turks...

Page 183: ...Warranty Regulatory and Contact Information 9 ...

Page 184: ...Warranty Regulatory and Contact Information 10 ...

Page 185: ...nizing 91 periods 56 recognizing one 59 signs of 56 storage of 89 storing IRR and NPV 98 viewing and editing 93 Chain mode calculations 27 Clearing backspace 29 messages in the display 30 Comma interchanging with period 43 Comma separator III Constants using 49 Cursor 29 Customer care and contact information 6 D Date calculations 101 Date format 99 bonds 106 Date keys 99 Decimal specifying display...

Page 186: ... 113 estimation of y 113 FC break even 109 FV 61 I YR 61 input 32 K 49 M 51 MAR margin 47 matdate bonds 105 mean of x weighted by y 113 means of x and y 113 MU markup 47 N 61 NFV 88 Nj 87 nom 79 NPV 88 number of days 99 off 23 on 23 one number functions 33 P YR 61 parentheses 28 percent 45 period comma 43 plus minus multiply divide 26 PMT 61 population standard deviation 113 PRC price business 47 ...

Page 187: ...erse 128 Student s T lower tail 131 Z and inverse 128 Q Questions I III R Random number and seed 127 Registers M register 51 using numbered registers 51 Regulatory Information 3 Reset II Rounding numbers 43 S Savings calculations 67 Scientific notation 43 Screen display iv Service II Statistics calculations that return two values 119 clearing data 114 entering data 114 keys used 113 linear regress...

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