Each year7500 is invested at 4 annual compound interest a Wh

Each year,$7,500 is invested at 4% annual compound interest a) What is the value of the investment portfolio after 20 years?After 25 years?After 30 years? b) Repeat part (a) with the investment at 5% annual compound interest c) Based answers to (a) and (b) what conclusion can be drawn regarding the impact of the interest earned versus the duration of the investment

Solution

a) Future value of the annuity is calculated using the formula :

After 20 years

F = A [ ( 1+r)ⁿ -1 ] / r

F = $ 7500 [ ( 1+0.04)²⁰ -1 ] /0.04

F = $ 223,335.58

After 25 years:

F = $ 7500 [ ( 1+0.04)²⁵-1 ] /0.04

F = $ 312,344.31

After 30 years :

F = $ 7500 [ ( 1+0.04)³⁰-1 ] /0.04

F = $ 420,637.03

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Repeating part (a) with the investment at 5% annual compound interest

After 20 years

F = $ 7500 [ ( 1+0.05)²⁰ -1 ] /0.05

F = $247,994.65

After 25 years: -

F = $ 7500 [ ( 1+0.05)²⁵-1 ] /0.05

F = $357,953.24

After 30 years: -

F = $ 7500 [ ( 1+0.05)³⁰-1 ] /0.05

F = $ 498,291.35

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Based on the analysis of part a and part b , it can be concluded that with the same duration , higher interest rate results in higher future value of the annuity .