After recieving an inheritance , a newly married couple invested $15250 for 10 years and recieved 9,150 in simple interest. What was the simple interest rate per year for the investment?

Question

part 2

 if that couple had been able to find an investment that paid 9% simple interest , how much more quickly would they have made that $9,150 in simple interest? State your answer in years and months.

Answer 1

Let S = sum of money at the end of the period

S_o = the initial money invested

I = interest rate

t = time

Then for this case S = S_o(1 + I)^t or 24,400 = 15250(1 + I)¹⁰ rearranging we have

24,400/15250 = (1 + I)¹⁰ 1.6 = (1 + I)¹⁰ now take the logarithm of both sides

log(1.6) =(10)log(1 + I) .0204 = log(1 + I) 1 + I = 1.0481

so,

Interest Rate = .0481 or 4.81%

Part 2: For 9% 24,400 = 15250(1 + .09)^t or 1.6 = (1.09)^t

or log(1.6) = (t)log(1.09) t = log(1.6)/log(1.09) = 5.45 years

So, they would have made the same amount about 4.5 years earlier.