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To help out with her retirement savings, Christine invests in an ordinary annuity that earns 4.8% interest, compounded annually. Payments will be made at the end of each year.

How much money does she need to pay into the annuity each year for the annuity to have a total value of $97,000 after 18 years?
Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

To help out with her retirement savings, Christine invests in an ordinary annuity-example-1
User JRV
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1 Answer

4 votes

Answer:

$3512.82

Explanation:

You want the value of the annual payment to an ordinary annuity earning 4.8% compounded annually, if the value after 18 years is $97,000.

Payment

The relationship between the payment P and the annuity value A is given by ...

A = P((1 +r)^t -1)/r . . . . . annual interest rate r for t years

Using the values in the problem statement, and solving for P, we have ...

P = Ar/((1 +r)^t -1)

P = $97000·0.048/(1.048^18 -1) ≈ $3512.82

Christine needs to pay in $3512.82 each year.

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To help out with her retirement savings, Christine invests in an ordinary annuity-example-1
User Tentux
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