Question

Andrew has saved $1,200,000 and is about to retire. If he can earn 3.75% annually and withdraw $70,000 at the beginning of each year, his fund can support __________ years of retirement life. (Rounded to two decimals)

Answer 1

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

1,200,000=1.0375*70,000[1-(1.0375)^-time period]/0.0375

1,200,000=1,936,666.67[1-(1.0375)^-time period]

[1-(1.0375)^-time period]=(1,200,000/1,936,666.67)

1-(1,200,000/1,936,666.67)=(1.0375)^-time period

(1.0375)^-time period=0.380378657

(1/1.0375)^time period=0.380378657

Taking log on both sides;

time period*log (1/1.0375)=log 0.380378657

time period=log 0.380378657/log (1/1.0375)

=26.26 years(Approx).