You are considering investing in a developing-country bank account that pays a nominal annual rate of 18%,compounded monthly.If you invest $5,000 at the beginning of each month,how many months will it take for your account to grow to $250,000? Round fractional years up.
A)23
B)27
C)32
D)38

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 $FV$ is the future value of the series, $P$ is the payment amount, $r$ is the monthly interest rate, and $n$ is the number of payments. The nominal annual rate is 18%, so the monthly rate is $18\% / 12 = 1.5\%$, or $0.015$ in decimal form. We want the future value ($FV$) to be $250,000, and we know that $P = $5,000$. Rearranging the formula to solve for $n$, and substituting the given values, we can solve for $n$. This requires iterative calculation or financial calculator. The correct answer, after performing the calculation, is closest to 38 months, considering the compounding effect and the monthly contributions.

You Are Considering Investing in a Developing-Country Bank Account That