Question

Clara is setting up a retirement fund, and she plans on depositing $5,000 per year in an investment that will pay 7% annual interest. How long will it take her to reach her retirement goal of $69,082? (Use appropriate factor(s) from the tables provided in your book.)

Answer 1

Answer:

It will take her 10 years to reach the retirement goal of $69,082.

Explanation:

Annuity can be explained as a constant stream of payments made at specific and/or special interval.

From the scenario painted, $5000 represents the annuity figure, as this is expected to be made annually at a 7% interest rate. The goal is to reach $69,082 in retirement fund. The $69,082 thus represents the future annuity. The $69,082 is the future value that is expected to have aggregated over time through the constant payment of the annuity figure of $5000 at a specified interest rate. Thus, this is called future value of annuity.

To get the future value of an annuity, we simply relate the future value, annuity payment and the interest factor together.

Thus, future value= annuity * interest factor.

Future value =$69,082

Annuity=$5,000

Hence, making interest factor the subject of the formula, we have:

Interest factor=$69,082/$5,000

Interest factor= 13.82(approximation)

Therefore, looking this up on the future value of an annuity table, at the specified rate of interest - 7%, the number of years we would arrive at is 10.