How many years before we run out of money? Sincerely, Luxury Challenged Marblehead, MA You can assume that the withdrawals (one per year) will sit in a checking account (no interest). The couple will use the account to cover the monthly shortfalls.

It will take t = 21.38 years for the money to run out

Explanation:

The question is incomplete. Kindly find the complete question below:

We have $1,000,000 invested in a high-grade, tax-free municipal-bond mutual fund. The return on the fund is 3.5% per year. We plan to make annual withdrawals from the mutual fund to cover the difference between our pension and Social Security income and our living expenses. How many years before we run out of money?

Answer:

Ct = P V * (1 + r) t

Ct = $1,000,000 * (1.035) ³

Ct = $1,108,718

Annual retirement shortfall = 12 * (monthly after tax pension + monthly after tax Social Security - monthly living expenses)

Annual retirement shortfall = 12 * ($7,500 + 1,500 - 15,000)

Annual retirement shortfall = - $72,000.

The withdrawals are an annuity due, so:

PV = C * ((1 / r) - {1 / [r (1 + r) t]}) * (1 + r) $1,108,718

= $72,000 * ((1 /.035) - {1 / [.035 (1 +.035) t]}) * (1 +.035)

14.878127 = (1 /.035) - {1 / [.035 (1 +.035) t]}13.693302

= 1 / [.035 (1 +.035) t]. 073028 /.035

= 1.035t

t = ln 2.086514 / ln 1.035t

t = 21.38 years