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Suppose an annuity pays 7.0% annual interest, compounded annually. If you invest $3,000 every year for 5 years, what percentage of the balance in the account is interest earned?

Round your answer to the nearest hundredth of a percent.

User Kolyunya
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1 Answer

14 votes
14 votes

Answer:

13.05%

Explanation:

The value of an ordinary annuity earning interest compounded annually is ...

A = P((1 +r)^n -1)/r . . . . . interest rate r for n years on principal payments P

For this account, the balance after 5 years will be ...

A = 3000((1 +.07)^5 -1)/0.07 = 3000·5.750739

The sum of payments is ...

payment total = 3000·5

Then the amount of interest is ...

3000·(5.750739 -5) = 3000·0.750739

and the fraction that is of the account balance is ...

(3000·0.750739)/(3000·5.750739) × 100% ≈ 13.05%

About 13.05% of the balance is interest earned.

User Jobo Fernandez
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