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# Determine APR

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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 \$21 million in 1977. That has grown to about \$140 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.)
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Mar 23, 2018

#1
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Just divide:

\$140 / \$21 = 6 2/3 - growth in the original amount over a period of 27 years.

[6 2/3]^(1/27*12) =[6 2/3]^(1/324) =1.00587248... - 1 x 1200 =7.05% - compounded monthly - the rate of return on the investment over a period of 27 years.

Mar 23, 2018
#2
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You can also solve it this way:

FV = PV x [1 + x]^(t*12)

140 = 21 x [1 + x]^(27*12)

140 = 21 x [1 + x]^324            divide both sides by 21

6 2/3 = [1+ x]^324                   take the log of both sides

0.82391... = 324 x log[1 +x]    divide both sides by 324

Log[1 + x] =0.002542928.....   take the exponent of both sides

[1 + x] = 10^0.002542928...

[1 + x] = 1.005872484421...    subtract 1 from both sides

x = 1.005872484421.... - 1 x 100 x 12

x = ~7.05% compounded monthly. The APR of this investment.

Mar 24, 2018