Question

You have been told that you need $21,600 today in order to have $100,000 when you retire 42 years from now. what rate of interest was used in the present value computation? assume interest is compounded annually.

Answer 1

You will have to use this formula:
log(1 + rate) = {log(total) -log(Principal)} ÷ Years
log(1 + rate) = {log(100,000) -log(21,600)} ÷ Years
log(1 + rate) = { 5 -4.3344537512} / Years
log(1 + rate) = { 0.6655462488} / 42
log(1 + rate) = 0.0158463393
1 + rate = 10^ 0.015846339
1 + rate = 1.0371613856
rate = .0371613856
rate = 3.71613856%

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Double-Check
Total = principal * (1 +rate)^years
Total = 21,600 * (1.0371613856)^42
Total = 21,600 *  4.6296296291  
Total = 100,000

Correct !!