Suppose your personal financial goal is to retire with a million dollars 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

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the future value of a series of annuity payments: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value ($1,000,000), $P$ is the monthly payment, $r$ is the monthly interest rate (5% annual rate divided by 12 months = 0.0041667), and $n$ is the total number of payments (43 years times 12 months/year = 516 payments). Rearranging the formula to solve for $P$, and plugging in the values, we find that the monthly payment required is approximately $552.13.

Suppose Your Personal Financial Goal Is to Retire with a Million