Your investment goal is to have $3,000,000 in 40 years for retirement. You decide to invest in a mutual fund today that pays 12% per year compounded monthly. How much must you invest at the end of each month to meet your investment goal? Round to the nearest $1.
A) $245
B) $255
C) $285
D) $305
E) $315

Question

Quizplus · Accepted Answer

To solve this, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value, $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. Here, $FV = \$3,000,000$, annual interest rate $= 12\%$, so monthly interest rate $r = \frac{12\%}{12} = 0.01$ (or 1%), and $n = 40 \times 12 = 480$ months. Rearranging the formula to solve for $P$, we get $P = \frac{FV}{\left( \frac{(1 + r)^n - 1}{r} \right)}$. Plugging in the values, $P = \frac{3,000,000}{\left( \frac{(1 + 0.01)^{480} - 1}{0.01} \right)}$, which approximately equals $255 when rounded to the nearest dollar.

Your Investment Goal Is to Have $3,000,000 in 40 Years