Sam got a job at the Brick. He plans to save $500 every month for 3 years to buy a car. The savings account earns 2.25% compounded monthly. If he puts the money in his savings account at the end of each month, how much interest is included in the future value of the annuity?

Question

Quizplus · Accepted Answer

The future value of an annuity can be calculated using the formula $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount per period, $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments. Here, $P = $500$, $r = \frac{2.25\%}{12} = 0.001875$, and $n = 3 \times 12 = 36$. Plugging these values into the formula gives the future value of the annuity. The interest included is the future value minus the total amount of payments made ($36 \times $500$).Calculating the future value:$$FV = 500 \times \frac{(1 + 0.001875)^{36} - 1}{0.001875} \approx 18603.37$$The total amount of payments made is:$$36 \times 500 = 18000$$The interest included is:$$18603.37 - 18000 = 603.37$$So, the correct answer is $603.37, which corresponds to choice E.

Sam Got a Job at the Brick