Question

Stacy Medavoy will invest $5,500 a year for 19 years in a fund that will earn 10% annual interest.

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If the first payment into the fund occurs today, what amount will be in the fund in 19 years? If the first payment occurs at year-end, what amount will be in the fund in 19 years? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

First payment today		$enter a dollar amount rounded to 0 decimal places
First payment at year-end

Answer 1

If the first payment occurs today:

Here, the deposits will be same every year, so it is an annuity. And the deposits start at the beginning of each year, so it is an annuity due. We need to find the future value of annuity due here. We will use the future value of annuity due table as per below:

Future value of annuity due (FVAD) = $5500 * FVAD (10%. 19 years)

where, FVAD (10%, 19 Years) is the future value of annuity due of $1 at 10% interest rate for 19 years. Its value from the future value of annuity due table is 56.2750.

Now, putting this value in the above formula, we get,

Future value of annuity due (FVAD) = $5500 * 56.2750

Future value of annuity due (FVAD) = $309513.

If the first payment occurs at year end:

Here, the deposits will be same every year, so it is an annuity. And the deposits start at the end of each year, so it is ordinary annuity. We need to find the future value of ordinary annuity here. We will use the future value of annuity table as per below:

Future value of annuity (FVA) = $5500 * FVA (10%. 19 years)

where, FVA (10%, 19 Years) is the future value of annuity or ordinary of $1 at 10% interest rate for 19 years. Its value from the future value of annuity table is 51.159.

Now, putting this value in the above formula, we get,

Future value of annuity (FVA) = $5500 * 51.159

Future value of annuity (FVA) = $281375.