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Abigail Nelson, a 25-year-old personal loan officer at First National Bank, understands the...

Question:

Abigail Nelson, a 25-year-old personal loan officer at First National Bank, understands the importance of starting early when it comes to saving for retirement. She has committed $3,000 per year for her retirement fund and assumes that she'll retire at the age of 65.

How much will she have accumulated when she turns 65 if she invests in equities and earns 8% on average?

Future Value of Annuity:

An annuity is a stream of uniform payments. The value of such stream in the future is known as the future value of annuity, and it can be calculated given an appropriate interest rate and the time period during which payments take place.

Answer and Explanation:

In this problem, we will use the formula for the future value of annuity that allows us to calculate the value of Abigail's periodic deposits when she turns 65.

{eq}Future\ Value = Deposit \times \dfrac{(1+r)^{n}-1}{r} {/eq}

Where r - periodic interest rate/rate of return; n - number of periods.

The number of periods, n, is equal to 65 - 25 = 40, and r is 8% per year, so:

{eq}Future\ Value = \$3,000 \times \dfrac{(1+0.08)^{40}-1}{0.08} {/eq}

{eq}Future\ Value = \$777,169.56 {/eq}

Therefore, Abigail will have $777,169.56 in her retirement fund when she turns 65.


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