Question

Assume you are to receive a 20-year annuity with annual payments of $60. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an account that pays 10 percent. What will be the value in your account at the end of Year 30?(FV twice) $6,854.81 $7,427.83 $8,709.88 $9,427.83

Answer #1

Future Value of Annuity = P[ (1+r)^{n} -1 ] /r

where p is periodic payment

r is int rate per period

n is no.of periods

Future value of annuity after 20 years = $ 60 [ ( 1 + 0.10
)^{20} -1 ] / 0.10

= $ 60 [ ( 1.10 )^{20} -1 ] / 0.10

= $ 60 [ 6.7275 -1 ] / 0.10

= $ 60 [ 5.7275 ] / 0.10

= $ 3,436.50

After 20 years, periodic payments are stopped, however int will be accumulated on this amount for the next 10 years

Future value for the next 10 years ( 30 years from now)

Amount = Principal ( 1 +r )^{n}

= $ 3,436.50 * ( 1 + 0.10 )^{10}

= $ 3,436.50 * ( 1.10 )^{10}

= $ 3,436.50 * 2.5937

= $ 8913.40

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