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%, compounded quarterly, how many months will her investment account last for approximately?

Question

Quizplus · Accepted Answer

First, we need to calculate the quarterly interest rate by dividing the annual interest rate by 4:

7% / 4 = 1.75%

Next, we need to calculate the number of periods (quarters) it will take for the account balance to be depleted. We can use the formula:

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

where PV is the present value (initial investment), PMT is the monthly payment, r is the quarterly interest rate, and n is the number of quarters.

Plugging in the values, we get:

$600,000 = $5,000 * ((1 - (1 + 0.0175)^-n) / 0.0175)

Simplifying:

120 = ((1 - 1.0175^-n) / 0.0175)

Multiplying both sides by 0.0175:

2.1 = 1 - 1.0175^-n

Subtracting 1 from both sides:

1.1 = 1.0175^-n

Taking the logarithm of both sides:

log(1.1) = -n * log(1.0175)

Dividing by -log(1.0175):

n = log(1.1) / log(1.0175)

Using a calculator:

n ≈ 206

Therefore, it will take approximately 206/12 = 17.17 years or 206 months for her investment account to last, which is closest to option D (206 months).

Your Mother Has Just Retired