My spouse and I are each 62 and hope to retire in 3 years. After retirement we will receive $5,000 per month after taxes from our employers pension plans and $1000 per month after taxes from Social Security. Unfortunately our monthly living expenses are $15,000. Our social obligations preclude further economies. We have $1,200,000 invested in a high-grade corporate-bond mutual fund. Unfortunately the after-tax return on the fund has dropped to 3.5% per year. We plan to make annual withdrawals from the fund to cover the difference between our pension and social security income and our living expenses.

How long will the money last?

• 15
• 15.4
• 15.8
• 16.4
• 16.8

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

Solution: D

Monthly amount to fund from the mutual fund = 15,000-6,000 = $9,000

PV of the fund in three years = $1, 200, 000 × 1.035³ = $1, 330, 461

Number of years that it will last:

$1330461 = 1.035 × 9000 × 12 × 10.035 × (1 -1.035^-T )

(assume you take the money out at the beginning of the year)

T = 16.4 years

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.