Find the balance of an increasing annuity in which a principal of $20 is invested each month for 40 years, compounded monthly at a rate of 8%.
A)$939.44
B)$11,878.94
C)$5,744.14
D)$70,305.62
E)$3,703.31

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 $20 for 40 years at an 8% annual interest rate, compounded monthly, we calculate the future value. The monthly interest rate is $0.08/12 = 0.0066667$, and the total number of payments is $40 \times 12 = 480$. Substituting these values into the formula gives a future value significantly higher than the highest option provided, indicating a need for the formula for an increasing annuity, not a standard annuity. The correct formula for an increasing annuity (or annuity due) takes into account the growth of the investment over time, leading to a much higher future value, which matches option D, $70,305.62, when correctly calculated.

Find the Balance of an Increasing Annuity in Which a Principal