Ashley will receive $525 at the beginning of every month for 20 years. She will invest...

Ashley will receive $525 at the beginning of every month for 20 years. She will invest this annuity at 11.0% compounded monthly. Calculate the Future Value of Ashley's annuity.

Round your answer to the nearest dollar. Do not include a dollar sign.

Your Answer:

Solutions

Expert Solution

Here, the receipts will be same every month, so it is an annuity. And the receipts start at the beginning of each month, so it is an annuity due. We need to calculate the future value of annuity due by the following formula:

FVAD = (1 + r) * P * ((1 + r)n - 1 / r)

where, FVAD is future value of annuity due, P is the periodical amount = $525, r is the rate of interest = 11% compounded monthly, so monthly rate = 11% / 12 = 0.91667% and n is the time period = 20 * 12 = 240 months

Now, putting these values in the above formula, we get,

FVAD = (1 + 0.916667%) * 525 * ((1 + 0.916667%)240 - 1 / 0.916667%)

FVAD = (1 + 0.0091667) * 525 * ((1 + 0.00916667)240 - 1 / 0.0091667)

FVAD = (1.00916667) * 525 * ((1.00916667)240 - 1 / 0.0091667)

FVAD = (1.0091667) * 525 * ((8.93501534917- 1) / 0.00916667)

FVAD = (1.0091667) * 525 * (7.93501534917 / 0.00916667)

FVAD = (1.00916667) * 525 * 865.638034944

FVAD = 458626

So, future value of annuity is 458626.

jeff jeffy answered 1 year ago

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