Final answer:
To determine the interest earned with semi-annual deposits into an account with semi-annual compounding, apply the formula for the future value of an ordinary annuity and then subtract the sum of the deposits from this total to get the interest earned.
Step-by-step explanation:
To calculate interest earned on a deposit made at the end of every six months, we can use the formula for the future value of an ordinary annuity. The formula is FV = P \times \frac{(1 + r)^n - 1}{r}, where FV is the future value of the annuity, P is the periodic payment, r is the periodic interest rate, and n is the total number of payments.
Given the periodic deposit of $620, an interest rate of 3.75\% compounded semi-annually, and a time span of 7 years, we will have the following values:
- Periodic payment P = $620
- Periodic interest rate r = \frac{3.75\%}{2} = 0.01875
- Number of periods n = 7 years \times 2 = 14
Plugging these into the formula, we get:
FV = $620 \times \frac{(1 + 0.01875)^{14} - 1}{0.01875} = $620 \times \frac{(1.01875)^{14} - 1}{0.01875}
After calculating the above expression, we subtract the sum of the periodic deposits from the future value to find the interest earned:
Total deposits = $620 \times 14 = $8,680
Interest earned = Future value - Total deposits
Calculating the exact amount and rounding to the nearest cent will give us the interest earned over the 7 year period.