Question

Q#2 a. What is the present value of $3,000 received 5 years fronm now, assuming 20% interest? b. What is the present value of an annuity of $50,000 received over 20 years, assuming 9% interest? c. What is the future value of $12,000, invested now at 10%, at maturity in 3 years? d. What is the future value of an annuity of $7,500, invested at 12%, at maturity in 5 years?

Answer 1

a)

Present value = Future value $\div$ ( 1+interest rate)ⁿ

Present value = $ 3000 $\div$ ( 1+ 0.20)⁵

Present value = $ 1,205.63

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b)

Present value of annuity = A [ ( 1+r)ⁿ -1 ] $\div$ r ( 1+r)ⁿ

Present value of annuity = $ 50,000 [ (1+0.09)²⁰ -1 ] $\div$ 0.09 ( 1+0.09)²⁰

Present value of annuity = $456,427.28

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c)

Future value = Present value ( 1 + interest rate)ⁿ

Future value = $ 12,000 ( 1+0.10)³

Future value = $ 15,972

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d) Future value of annuity = A [ (1+r)ⁿ -1 ] $\div$ r

Future value of annuity = $ 7500 [ (1+0.12)⁵ -1 ] $\div$ 0.12

Future value of annuity = $ 47,646.36

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