Question

$100 is invested for 20 years. During the first 10 years, the annual rate of 6%. During the last 10 years, the annual rate is 5%. How much interest is compounded during the last 10 years on the interest compounded during the first 10 years (in dollars)?

Answer 1

Amount Invested today = $100

Interest rate for first 10 years = 6% per annum

Calculating Future Value of Investment after first 10 years:-

Future Value = Invested Amount*(1+Interest Rate)^n

where,Interest Rate = 6%

n = no of years = 10

FV = $100*(1+0.06)^10

=$100*1.79085

= $179.085

So, Value after first 10 years = $179.085

Interest Compounded during the first 10 years = $179.085 - $100

=$79.085

Future Value of Interest Compounded during the first 10 years = $79.085*(1+0.05)^10

=$79.085*1.628895

= $128.82

So, the amount of Interest is compounded during the last 10 years on the interest compounded during the first 10 years (in dollars) = $128.82 - $79.085

=$49.74