$500 is contributed at the beginning of each period on a semi-annual basis for 5 years. If the rate of interest is 5% compounded semi-annually, determine how much interest was earned over this time.

Question

Quizplus · Accepted Answer

The interest earned can be calculated using the formula for the future value of a series of annuities. The formula is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the total number of payments. Here, $P = $500$, $r = 0.05/2 = 0.025$ (since the interest is compounded semi-annually), and $n = 5 \times 2 = 10$ (since payments are made semi-annually over 5 years). Plugging these values into the formula gives $FV = 500 \times \frac{(1 + 0.025)^{10} - 1}{0.025}$, which calculates to approximately $5,741.73. The interest earned is the future value minus the total amount contributed, which is $5,741.73 - 5,000 = $741.73$.

$500 Is Contributed at the Beginning of Each Period on a Semi-Annual