Question

1 year(s) ago, Liam invested 26,668 dollars. He has earned and will earn 12.3 percent per year in compound interest. If Zoey invests 47,298 dollars in 2 year(s) from today and earns simple interest, then how much simple interest per year must Zoey earn to have the same amount of money in 6 years from today as Liam 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

Liam Amount invested 1 year ago=$26668

Amount with Liam 6 years from today, i.e. amount invested for 7 years=amount invested*(1+interest rate)^ number of years

=26668*(1.123)^7=$60068.77

Total simple interest to be earned by Zoey=Total amount with Liam-Total investment by Zoey=$60068.77-$47298=$12770.77

Zoey has to earn this interest in 4 years as she will start investing two years from today and she should have some money as Liam 6 years from today, so

Simple interest=Principal*interest rate/100* number of years

Or, 12770.77=47298* interest rate/100*4

or, interest rate=12770.77*100*1/4*1/47298=6.75

Hence interest to be earned=6.75% or 0.0675