Question

Suppose your personal financial goal is to retire with $1 million in your savings account. How much must you deposit monthly in an account paying 5% a year (with interest being compounded monthly and your deposits occurring at the end of the month), to accumulate $1,000,000 by your 65th birthday if you begin your deposits on your 22nd birthday? (Note: Assume that you started with no savings in the account prior to your first deposit at age 22 and you do not make a deposit on your 65th birthday.)

A) $552.13

B) $701.90

C) $21,282.95

D) $186,354.63

Answer 1

The amount is computed as shown below:

Future value = Monthly deposits x [ [ (1 + r)ⁿ - 1 ] / r ]

r is computed as follows:

= 5% / 12

= 0.004166667

n is computed as follows:

= (65 - 22) x 12 months

= 516

So, the monthly deposits will be as follows:

$ 1,000,000 = Monthly deposits x [[ (1 + 0.004166667)⁵¹⁶ - 1 ] / 0.004166667 ]

$ 1,000,000 = Monthly deposits x 1,811.183227

Monthly deposits = $ 1,000,000 / 1,811.183227

Monthly deposits = $ 552.13 Approximately

So, the correct answer is option A.

Feel free to ask in case of any query relating to this question