Answer:
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
