5 Find the Value of an Annuity
Solve the problem. Round to the nearest dollar if needed.
-Geraldo deposits $100 each month into an account paying annual interest of 5.5% compounded monthly. How much will his account have in it at the end of 9 years?
A)$13,934
B)$1126
C)$13,780
D)$14,063

Question

Quizplus · Accepted Answer

The value of an annuity can be calculated using the formula for the future value of an annuity: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value of the annuity, $P$ is the payment amount per period, $r$ is the interest rate per period, and $n$ is the total number of payments. In this case, $P = $100$, $r = \frac{5.5\%}{12} = 0.0045833$ (since the interest is compounded monthly), and $n = 9 \times 12 = 108$ (since there are 9 years of monthly payments). Plugging these values into the formula gives a future value of approximately $13,934, hence option A is correct.