Julian has been investing $1,500 at the beginning of every six months for a long time and earning 11% compounded semiannually. His investments have now accumulated to $766,715. How long ago did he make the first $1,500 payment?

Question

Quizplus · Accepted Answer

The problem can be solved using the formula for the future value of a series: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value of the series, $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the total number of payments. Given that $FV = 766,715$, $P = 1,500$, $r = 0.055$ (since 11% annual interest compounded semiannually gives a per period rate of 11%/2 = 5.5% or 0.055), we need to find $n$. Rearranging the formula to solve for $n$ and substituting the given values, we can solve for $n$ and then divide by 2 (since there are 2 periods per year) to find the number of years. This calculation will show that Julian started investing 31 years ago.

Julian Has Been Investing $1,500 at the Beginning of Every