Consider three investment plans at an annual rate of 9.38%. • Investor A: Invest
ID: 1216403 • Letter: C
Question
Consider three investment plans at an annual rate of 9.38%. • Investor A: Invest $2000 per year for the first 10 years of your career. At the end of 10 years, make no further investments, but reinvest the amount accumulated at the end of 10 years for the next 31 years. • Investor B: Do nothing for the first 10 years. Then start investing $2000 per year for the next 31 years. • Investor C: Invest $2000 per year for the entire 41 years. Note that all investments are made at the beginning of each year, the first deposit will be made at the beginning of age 25 (n=0), and you want to calculate the balance at age of 65 (n=41).Explanation / Answer
Investor A
Future value of Annuity due
F = A [( 1+r)n -1 ] / r [ ( 1+r) ]
F = $ 2,000 [ ( 1+0.0938)10 -1 ] / 0.0938 [ ( 1+0.0938) ]
F = $ 33,844.88
This is reinvestd at the end of 10 years for the next 31 years
The future of the reinvested amount at the end of 31 years = $ 33,844.88 ( 1+0.0938)10
The future of the reinvested amount at the end of 31 years = $ 82,960.67
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Investor 2 :
F = A [( 1+r)n -1 ] / r [ ( 1+r) ]
F = $ 2000 [ ( 1+0.0938)31 -1 ] / 0.0938 [ ( 1+0.0938) ]
F = $ 352,377.49
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Investor 3
F = A [( 1+r)n -1 ] / r [ ( 1+r) ]
F = $ 2000 [ ( 1+0.0938)41 -1 ] /0.0938 [ ( 1+0.0938) ]
F = $ 897,593.48