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

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.