A small business owner contributes $2,000 at the end of each quarter to a retirement account that earns an annual rate of 6.5% compounded quarterly. How long will it be until the account is worth $250,000? Round your answer to the nearest whole number.

Question

A small business owner contributes $2,000 at the end of each quarter to a retirement account that earns an annual rate of 6.5% compounded quarterly. How long will it be until the account is worth $250,000? Round your answer to the nearest whole number. ​

Quizplus · Accepted Answer

The account grows according to the formula for the future value of an annuity: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods. Here, $P = 2000$, $r = 0.065/4 = 0.01625$ (since the interest is compounded quarterly), and $FV = 250,000$. Solving for $n$, we find that it takes approximately 69 quarters to reach $250,000.

A Small Business Owner Contributes $2,000 at the End of Each