Question

Bridgette wants to retire 28 years from now. She decides to start saving $400 each month into a Roth IRA starting at the end of this month. If the IRA is expected to earn an average annual return of 10% compounded monthly, how much will she have in the account at the end of 28 years? Round to two decimal places.

Years	0	4	8	12	16	20	22	24	28
Cash Flow		$400	$400	$400	$400	$400	$400	$400	$400

Answer 1

Your timeline is incorrect. Your timeline states that $400 is being put at the end of the YEAR. However, question states that $400 is being out at the end of every month.

There are 12 months in a year. theerfore, total number of periods = 28 * 12 = 336

It should be:

1 - 400

2 - 400

3 - 400

.

.

.

.

336 - 400

It should be months instead of years.

I will also calculate the future value.

Monthly rate = 10% / 12 = 0.833333%

Future value = Monthly payments * [(1 + r)^n - 1] / r

Future value = 400 * [(1 + 0.00833333)^336 - 1] / 0.00833333

Future value = 400 * [16.254936 - 1] / 0.00833333

Future value = 400 * 1,830.593088

Future value = $732,237.81

She will have $732,237.81