Your mother has just retired.The balance in her investment account is $600,000 and she wants to receive monthly payments of $5,000.If she receives the payments at the end of the month,and the current interest rate is 7 percent,compounded quarterly,how many months will her investment account last for?

Question

Quizplus · Accepted Answer

To determine how many months the investment account will last, we need to calculate the future value of the account using the given interest rate and payment amount, and then divide the total by the monthly payments to find how many months it will take to reach that total.

First, we need to calculate the quarterly interest rate:

r = (1 + 0.07/4)^(4/12) - 1
r = 0.0171 or 1.71%

Next, we can use the formula for the future value of an annuity to find the total balance after her retirement account has been fully depleted:

FV = PMT * ((1 + r)^n - 1)/r

Where:
PMT = $5,000
r = 0.0171
FV = $600,000

$600,000 = $5,000 * ((1 + 0.0171)^n - 1)/0.0171

Solving for n:

n = (ln(1 + 0.0171*600,000/5,000))/ln(1 + 0.0171)

n = 206.04 or approximately 206 months

Therefore, the investment account will last for approximately 206 months, or about 17 years and 2 months. The correct answer is D.

Your Mother Has Just Retired