Question

Jim invests 2,000 at an effective annual interest rate of 17% for 10 years. Interest is...

Jim invests 2,000 at an effective annual interest rate of 17% for 10 years.
Interest is payable annually and is reinvested at an annual rate of 11%. At the end of 10 years, Jim’s accumulated interest is 5685.48.

Harold invests 150 at the end of each year for 20 years at an effective annual interest rate of 14%. Interest is payable annually and is reinvested at an effective annual interest rate of 11%.

Calculate Harold’s accumulated interest at the end of 20 years.

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Answer #1

Interest amount = Principal x rate x time in years

Annual interest earned by Harold = $ 150 x 14 % x 1 = $ 150 x 0.14 = $ 21

Accumulated interest at the end of 20 years can be computed using formula for FV of annuity as:

FV = Annual cash investment x FVIFA (11 %, 20)

      = $ 21 x [{(1+0.11)20 – 1}/0.11]

     = $ 21 x [{(1.11)20 – 1}/0.11]

     = $ 21 x [{(8.06231153612915 – 1}/0.11]

     = $ 21 x [(7.06231153612915)/0.11]

     = $ 21 x 64.2028321466287

     = $ 1,348.2594750792 or $ 1,348.26

Accumulated interest of Harold at the end of 20 years is $ 1,348.26

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