Find the balance of an increasing annuity in which a principal of $300 is invested each month for 33 years, compounded monthly at a rate of 8%.
A)$42,454.33
B)$583,960.90
C)$63,895.28
D)$123,835.77
E)$11,406.08

Question

Quizplus · Accepted Answer

The balance of an increasing annuity can be calculated using the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the monthly interest rate, and $n$ is the total number of payments. Given a monthly investment of $300 for 33 years at an annual interest rate of 8% compounded monthly, we first convert the annual rate to a monthly rate by dividing by 12, resulting in $r = 0.08/12 = 0.0066667$. The total number of payments, $n$, is $33 \times 12 = 396$. Plugging these values into the formula gives a future value, which closely matches choice B, $583,960.90, indicating a significant growth due to the power of compound interest over a long period.

Find the Balance of an Increasing Annuity in Which a Principal