Question

Problem #8 (TVM): Tom's best friend, Joe, works for a company that was just acquired. He lost hi job. Joe was given a severance payment of $365,000, which he invested at a 7.5% annual rate. He now plans to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. How many years will it take to exhaust his funds, i.e., run the account down to zero?

Answer 1

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

365,000=35000[1-(1.075)^-time period]/0.075

365,000=466666.667[1-(1.075)^-time period]

(365,000/466666.667)=[1-(1.075)^-time period]

[1-(1.075)^-time period]=0.782142857

(1.075)^-time period=1-0.782142857

(1/1.075)^time period=0.217857143

Taking log on both sides;

time period*log (1/1.075)=log0.217857143

time period=log0.217857143/log (1/1.075)

=21.07 years(Approx).