$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.

A) $500.00
B) $462.36
C) $402.00
D) $741.73
E) $302.00

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 .