# At the beginning of each period for 10 years, Merl Agnes invests $500 semiannually at 6%. What is...

## Question:

At the beginning of each period for 10 years, Merl Agnes invests $500 semiannually at 6%. What is the cash value of this annuity due at the end of year 10?

## Future Value of Annuity Due:

When an investment is made at the beginning of each period, the future value is calculated using the formula for future value of annuity due. On the other hand, when an investment is made at the end of each period, the future value is calculated using the formula for future value of annuity. An annuity is a steady stream of investment or cash flows that continues for a definite time period.

## Answer and Explanation:

.

Given -

- Investment = $500
- Rate = 6% = 6 / 2 = 3% { semi-annual }
- Time = 10 years = 10 * 2 = 20 periods { semi-annual }

The formula for future value of annuity due is given as follows -

- Future Value of Annuity Due = {eq}( 1 + r ) * P [ ( 1 + r ) ^ n - 1 / r ] {/eq}

- Future Value of Annuity Due = {eq}( 1 + 0.03 ) * 500 [ ( 1 + 0.03 ) ^ 20 - 1 / 0.03 ] {/eq}

- Future Value of Annuity Due = {eq}$13,838.24 {/eq}

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