Find the amount accumulated in the increasing annuity of $200 deposited monthly for 5 years at 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
A)$92,929.34
B) $24,720.00
C) $12,929.34
D) $4,646.47
E) $1,292.93

Question

Find the amount accumulated in the increasing annuity of $200 deposited monthly for 5 years at 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​
A)$92,929.34
B) $24,720.00
C) $12,929.34
D) $4,646.47
E) $1,292.93

Quizplus · Accepted Answer

To find the amount accumulated in an increasing annuity, we use the future value of an annuity formula adjusted for monthly deposits and compounding. The formula for the future value of an annuity when compounding and deposits are made at the same frequency is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount per period, $r$ is the interest rate per period, and $n$ is the total number of payments. For monthly deposits at an annual interest rate, $r = \frac{0.03}{12}$ and $n = 5 \times 12 = 60$. Plugging in the values: $FV = 200 \times \frac{(1 + \frac{0.03}{12})^{60} - 1}{\frac{0.03}{12}}$, calculating this gives a future value close to $12,929.34, which matches option C.

Find the Amount Accumulated in the Increasing Annuity of $200