Question

4 year(s) ago, Isaac invested 79,304 dollars. He has earned and will earn 9.05 percent per year in compound interest. If Fatima invests 130,108 dollars in 2 year(s) from today and earns simple interest, then how much simple interest per year must Fatima earn to have the same amount of money in 6 years from today as Isaac will have in 6 years from today? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Sol:

Isaac investment value (C) =  $79,304

Total investment period (n) = 10 years

Interest rate (r) = 9.05% per year

Future value (FV) of Isaac investment:

FV = C x (1 + r)^n

FV = 79,304 x (1 + 9.05%)^10

FV = 79,304 x (1.0905)^10

FV = $188,604.39

Therefore Future value (FV) of Isaac investment will be $188,604.39

Fatima investment value (C) = $130,108

Period (n) = 4 years

To determine simple interest to earned by Fatima in one year:

130,108 x (1 + r x n) = 188,604.39

(1 + r x 4) = 188,604.39 / 130,108

(1 + r x 4) = 1.4496

(r x 4) = 1.4496 - 1

(r x 4) = 0.4496

r = 0.4496 / 4 = 0.1124

Therefore simple interest to earned by Fatima in one year = 0.1124