Question

James invests 2,000 at an effective annual interest rate of 17 percent for 10 years. Interest is payable annually and is reinvested at an effective annual rate of 11 percent. At the end of 10 years, James’ accumulated interest is 5,685.48 Peter invests 150 at the end of each year for 20 years at an effective annual interest rate of 14 percent. Interest is payable annually and is reinvested at an effective annual rate of 11 percent. Calculate Peter’s accumulated interest at the end of 20 years.

Answer 1

Answer:

$1,195.73

Explanation:

Peter invests $150 at the end of each year for the next 20 years where he gets a return of 14 percent, The amount of interest earned each year is

150 x 0.14 = $21

Since the first interest payment is to be reinvested at the end of the first year of investment, this payment would be reinvested for the next 19 years

We can find the future value of annuity formula to compute the interest earned on reinvested interest

PMT = $21

i = 11%

n = 19

FVA = PMT [(1+i)^n -1]/i

FVA = 21 [(1+0.11)^19 - 1]/0.11

FVA = 21 [1.11^19 - 1]/0.11

FVA = 21 x 6.26334 / 0.11 = 1,195.73