Question

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.

Answer 1

$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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