Question

4 year(s) ago, Carl invested 65,612 dollars. He has earned and will earn 6.94 percent per year in compound interest. If Grace invests 105,332 dollars in 3 year(s) from today and earns simple interest, then how much simple interest per year must Grace earn to have the same amount of money in 9 years from today as Carl will have in 9 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

Carl has invested $ 66,612 four years ago @ 6.94% per year compounded interest,

Then total amount after four years would be as under :

A = P (1+r/n)nt

Where as, A = Furture Value, P = Present Value or principal amount, r = Interest rate, n= number of times that is compounded in one t, t = time

$ 65,612 (1+0.0694/1)1x4

= $ 85,811.20

The other part of the question is as under :

If Grace invested $ 105,332 in 3 years from now,

It is assumed that Carl will earn 6.94% interest per year for nine years, hence the interest for nine years would be as under

Amount of interest earned is $ 105,332 x 0.0694 X 9 = $ 65,790.3672

Therefore total interest earned is $ 65,790.3672

hence interest would be divided in three years for simple interest = $ 65,790.3672 / 3 = $ 21930.1224

Thus, to earn total interest in 9 years at simple interest rate would be (Interest Rate x 9) / 3

Therefore at present interest rate (0.0694*9) / 3 = 0.2082

Hence = $ 105,332 * 0.2082 * 3 = $ 65,790.3672