Question

You have just been given a $454,000, which you decide to invest at an APR of 6.7 percent. If you were to withdraw $38,500 at the end of each year, starting at the end of this year, how many years will it take you to exhaust these funds?

Answer 1

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

454000=38500[1-(1.067)^-time period]/0.067

454000=574,626.8657[1-(1.067)^-time period]

(454000/574,626.8657)=[1-(1.067)^-time period]

1-(454000/574,626.8657)=(1.067)^-time period

0.209922078=(1/1.067)^time period

Taking log on both sides;

log 0.209922078=time period*log (1/1.067)

time period=log 0.209922078/log (1/1.067)

=24.07 years(Approx).