Derek contributed $200 per month for twenty years at an interest rate of 3.9% compounded semi-annually. Determine how much interest was earned over the twenty year period.
A) $24,282.30
B) $25,282.30
C) $26,282.30
D) $27,282.30
E) $28,282.30

Question

Quizplus · Accepted Answer

The total amount accumulated, using the future value of a series formula, is calculated as $FV = P \times \frac{((1 + r)^n - 1)}{r}$, where $P$ is the monthly contribution, $r$ is the monthly interest rate, and $n$ is the total number of contributions. Since the interest is compounded semi-annually but contributions are monthly, we adjust the annual interest rate of 3.9% to a monthly rate by dividing by 12, after adjusting for semi-annual compounding. However, the direct application of this formula in its basic form might not account for the semi-annual compounding directly without further adjustments for the effective monthly rate. The total contributions over 20 years are $200 \times 12 \times 20 = 48,000$. The future value of these contributions can be calculated using a financial calculator or spreadsheet by inputting the appropriate values for monthly contributions, time period, and interest rate adjusted for the compounding frequency. The interest earned is the difference between the future value and the total contributions. Given the options and the nature of the problem, without the exact calculation provided here, the correct answer involves understanding that the total amount accumulated minus the principal (total contributions) gives the interest earned, which matches closest to option A, assuming typical methods for calculating compound interest on such regular contributions.

Derek Contributed $200 Per Month for Twenty Years at an Interest