Solve.
-After working for 25 years you would like to have $800,000 in an annuity for early retirement. If theannual interest rate is 7.5%, compounded monthly, what will your monthly deposit need to be?
A)$911.93
B)$2666.67
C)$3088.48
D)$1146.98

Question

Quizplus · Accepted Answer

To find the monthly deposit required to reach a future value of $800,000 in an annuity, we use the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the total number of payments. Rearranging the formula to solve for P gives us $P = FV \times \frac{r}{(1 + r)^n - 1}$. Given an annual interest rate of 7.5%, the monthly interest rate is $0.075/12 = 0.00625$. The total number of payments for 25 years with monthly deposits is $25 \times 12 = 300$. Plugging these values into the formula gives $P = 800,000 \times \frac{0.00625}{(1 + 0.00625)^{300} - 1}$, which calculates to approximately $911.93.

Solve. -After Working for 25 Years You Would Like to Have