| |
|
Conventional Method
|
HP-80 Method
|
|
Use basic formula:
|
Key in:
|
S = P(1 + i )n
|
7 n 10000 PV 15000 FV i
|
|
(1 + i)n =
|
S
|
|
|
|
|
P
|
|
Find answer displayed:
5.96 %
|
|
Where:
|
|
|
S = future value
|
|
|
P = present value
|
|
|
i = effective periodic rate
|
|
|
n = number of periods
|
|
| |
|
Thus:
|
|
|
(1 + i)n =
|
$15000
|
= 1.50
|
|
|
|
$10000
|
|
|
|
Next, consult compound interest table to find the table value closest to 1.5000000. The table value of 5% for seven years is 1.4071004227,
while the value for 6% is 1.5036302590. Therefore, the exact annual rate of return is somewhere between 5% and 6%.
|
|
| |
|
Now for interpolation (note that since method used is linear interpolation, the answer is only approximate). Let:
|
|
| |
|
X = amount between actual and low value .01 (or 1 %) = difference between two table values
|
|
|
0928995773 = difference between lower table amount of 1.4071004227 and actual of 1.50
|
|
|
.0965298363 = difference between higher and lower table amounts.
|
|
| |
|
Then, set up the equation as a proportion:
|
|
|
X
|
=
|
.0928995773
|
|
|
|
|
|
.01
|
.0965298363
|
|
|
| |
|
Cross-multiply:
|
|
|
.0965298363X = .01 × .0928995773
|
|
|
= .000928995773
|
|
| |
|
Divide by .0965298363:
|
|
|
X =
|
.000928995773
|
|
|
|
|
.0965298363
|
|
|
|
= .00962392363448 or .96%
|
|
| |
|
Finally:
|
|
|
Annual rate of return = lower table rate of 5% + .96% or 5.96%.
|
|
|
|
|
