44
COMPOUND INTEREST
Calculate the new balance on a deposit which is compounded quarterly for 4 years as
a given annual interest rate.
SOLUTION:
1. Calculate the quarterly interest rate.
2. Calculate the new balance (principal plus interest)
FORMULA:
New balance = P (1 + i)
n
Where
P =
amount of deposit (principal)
i
=
interest rate per period
n
=
number of years
×
4
EXAMPLE:
If
P =
$6,150
i
=
5% annum
÷
4 periods = 0.0125
n
=
16 (4 years
×
4)
Then 6,150 (1.0125)
16
.=. $7,502.32 (New Balance)
OPERATION
DISPLAY
.05
0.05
0.05
÷
4
4. =
0.0125
∗
Quarterly int. rate
0.0125
0.0125
0.0125 +
1
1.0125
1. +
1.0125
◊
(1 + i)
1.0125
1.0125
×
1.0125 =
1.02515625
∗
(1 + i)
2
1.02515625
1.02515625
1.02515625
×
1.02515625 =
1.05094533691
∗
(1 + i)
4
1.05094533691
1.05094533691
1.05094533691
×
1.05094533691 =
1.10448610117
∗
(1 + i)
8
1.10448610117
1.10448610117
1.10448610117
×
1.10448610117 =
1.21988954767
∗
(1 + i)
16
1.21988954767
1.21988954767
1.21988954767
×
6150
6,150. =
7,502.32071817
∗
7,502.32071817
CS-2850A-Cal
05.5.10, 4:05 PM
Page 44
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