Question

4 year(s) ago, Liam invested 33,113 dollars. He has earned and will earn 5.81 percent per year in compound interest. If Emily invests 32,206 dollars in 1 year(s) from today and earns simple interest, then how much simple interest per year must Emily earn to have the same amount of money in 8 years from today as Liam will have in 8 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

Amount was invested by Liam 4 years ago, total period of investment = 4+8 = 12 years

Amount that Liam will have 8 years from today = 33,113(1+0.0581)¹²

= $65,210.74

Emily will invest 1 year from today, hence total period of investment = 7 years

Amount of interest required to reach same amount as Liam = Total Amount – Principal Amount

= $65,210.74 – 32,206

= $33,004.74

Let the interest rate be x

32,206*x%*7 = 33,004.74

X = 0.1464

Hence, required interest rate is 0.1464