This exercise is designed to be solved using technology such as calculators or computer spreadsheets.
A news article published in 2004 said that a country's House of Representatives passed a bill to distribute funds to members of a tribe. Here is an excerpt from that article:
The Claims Commission decided the tribe lost much of their land to gradual encroachment. The tribe was awarded $25 million in 1977. That has grown to about $160 million through compound interest, but the tribe never took the money.
Assume monthly compounding and determine the APR that would give this growth in the award over the 27 years from 1977 to 2004. Note: This can also be solved without technology, using algebra. (Round your answer to two decimal places.)
Here is a simple solution:
$160 / $25 =6.4 - growth in the original amount over 27 years
6.4^(1/27*12) =6.4^(1/324) =1.005745758.. - 1 x 1200 =6.89% comp. monthly over 27 years.
Using Algebra:
FV = PV x [ 1 + R]^324
160 =25 x [1 + R]^324 divide both sides by 25
6.4 = [1 + R]^324 take the log of both sides
Log[1 + R] = 0.00248820....
[1 + R] = 10^0.00248820
[1 + R] =1.005745758
R =1.005745758 - 1 x 12 x 100
R =6.89% - compounded monthly.
