Question

What is the accumulated (future) sum of monthly contributions of
$500 invested at an average return of 5% p.a. over 30 years? What
if the average return increases to 8% from the 16^{th}
year?

Answer #1

We have to find the future value of a series of annuity. We will make use of the FV function in excel.

Accumulated (future) sum of monthly contributions of $500 invested at an average return of 5% p.a. over 30 years = FV (Rate, Period, PMT, PV) = FV (5%/12, 12 x 30, -500, 0) = $ 416,129.32

If average return increases to 8% from the 16th yer, then we will have to do it in two steps.

Step 1: Accumulated (future) sum of monthly contributions of $500 invested at an average return of 5% p.a. over 15 years = FV (Rate, Period, PMT, PV) = FV (5%/12, 12 x 15, -500, 0) = $ 133,644.47

This will now be the PV for the next 15 years.

Hence, accumulated value at the end of 30 years = FV (Rate, Period, PMT, PV) = FV (8%/12, 12 x 15, -500, -133644.47) = $ 614,970.89

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