Alessandro has saved $800,000 in his retirement account, which earns an annual interest rate of 5% He plans to withdraw from the account each month for 30 years. What will Alessandro's approximate monthly payout, monthly interest, and total number of payments be? Use the formula P=PV⋅(r)/(1−(1+r)^−n)
Answer
A
4 dollars comma 294 point 5 7, with a monthly interest rate of 0 point 0 0 4 2 and 360 total payments
B
4 dollars comma 512 point 9 0, with a monthly interest rate of 0 point 0 0 3 1 and 360 total payments
C
4 dollars comma 100 point 0 0, with a monthly interest rate of 0 point 0 0 2 7 and 300 total payments
D
4 dollars comma 050 point 2 5, with a monthly interest rate of 0 point 0 0 3 3 and 360 total payments
Explanation
There are 12 monthly payments per year, so 30 years gives 30 × 12 = 360 payments. The monthly interest rate is 0.05 ÷ 12 ≈ 0.0042. Substituting PV = $800,000, r ≈ 0.004167, and n = 360 into the formula gives a monthly payout of about $4,295, matching choice D, $4,294.57.
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