After saving diligently your entire career, you and your spouse are ready to retire with a nest egg of $500,000. You need to invest this money in a mix of stocks and bonds that will allow you to earn $4,000 per month for 30 years. What annual interest rate (APR) do you need to earn?
A) 6.92%
B) 7.45%
C) 8.94%
D) 9.17%

Question

Quizplus · Accepted Answer

To determine the annual interest rate required, we can use the present value annuity formula:

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

Where:
PV = present value (in this case, $500,000)
C = monthly payment (in this case, $4,000)
r = annual interest rate
n = total number of periods (in this case, 30 x 12 = 360 months)

Substituting the values, we get:

500,000 = 4,000 * (1 - (1 + r/12)^-360) / (r/12)

Simplifying:

125 = (1 - (1 + r/12)^-360) / (r/12)

Multiplying both sides by (r/12):

125r/12 = 1 - (1 + r/12)^-360

We can then solve for r using trial and error or an online calculator. The answer is approximately 8.94%, which is option C.

After Saving Diligently Your Entire Career, You and Your Spouse