If you save $250 at the beginning of every month how long will it take to accumulate $250,000 at a rate of 9% compounded monthly?

Question

Quizplus · Accepted Answer

To solve this, we use the future value of a series formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the monthly interest rate, and $n$ is the number of payments. Rearranging to solve for $n$, we get $n = \frac{\log(\frac{FV \times r}{P} + 1)}{\log(1 + r)}$. Given $FV = 250,000$, $P = 250$, and an annual interest rate of 9% (or a monthly rate of $0.09/12$), we find $n$ to be approximately 286 months.

If You Save $250 at the Beginning of Every Month