Question

assume that you reached retirement, you have accumlated a 4,000,000 nest. Assume you live on 300,000 per year and you only earn 4% per year. How many years will you run out of money? show work

Answer 1

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

4,000,000=300,000[1-(1.04)^-time period]/0.04

4,000,000=7,500,000[1-(1.04)^-time period]

(4,000,000/7,500,000)=[1-(1.04)^-time period]

[1-(1.04)^-time period]=0.533333333

1-0.533333333=(1.04)^-time period

(1.04)^-time period=0.4667

(1/1.04)^time period=0.4667

Taking log on both sides;

time period*log (1/1.04)=log 0.4667

time period=log 0.4667/log (1/1.04)

=19.43 years(Approx)