If you have $45,000 earning 9.6% compounded monthly, how much money could you take out of the investment at the end of every year for 10 years?

Question

Quizplus · Accepted Answer

The correct answer can be found using the formula for the annual withdrawal from an investment that earns compound interest, which is a type of annuity calculation. The formula for the annual withdrawal can be derived from the present value of an annuity formula, which is:$$PMT = PV \times \frac{i}{1 - (1 + i)^{-n}}$$Where:- $PMT$ is the annual payment (withdrawal),- $PV$ is the present value of the annuity (initial investment),- $i$ is the monthly interest rate (annual interest rate divided by 12),- $n$ is the total number of payments (number of years times 12, for monthly compounding).Given:- $PV = \$45,000$,- Annual interest rate = 9.6% or 0.096,- Compounded monthly, so $i = 0.096 / 12$,- $n = 10 \times 12 = 120$ months.Plugging these values into the formula gives us the annual withdrawal amount. Calculating this using the given values:$$i = \frac{0.096}{12} = 0.008$$$$n = 10 \times 12 = 120$$$$PMT = 45000 \times \frac{0.008}{1 - (1 + 0.008)^{-120}}$$$$PMT ≈ \$7,334$$Therefore, the correct answer is $7,334, which corresponds to choice B.

If You Have $45,000 Earning 9