Clarence has been investing $1,000 at the end of every year at 11% compounded annually. With today's contribution his investment has grown to $44,500. How many years ago did he make the first contribution?

Question

Quizplus · Accepted Answer

The formula for the future value of a series of annuities (regular payments or contributions) is given by $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value of the annuity, $P$ is the payment amount, $r$ is the annual interest rate, and $n$ is the number of payments. Rearranging the formula to solve for $n$, we get $n = \frac{\log(\frac{FV \times r}{P} + 1)}{\log(1 + r)}$. Substituting $FV = 44500$, $P = 1000$, and $r = 0.11$, we can solve for $n$. The calculation gives a value close to 17, indicating that Clarence made his first contribution 17 years ago.

Clarence Has Been Investing $1,000 at the End of Every