Question

Your account is worth $100,000 today. You want to withdrawal $15,000 each year. How many years will you be able to withdrawal money if your account makes 8% interest?

Answer 1

Using the formula of Present value of annuity,

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

100,000=15,000[1-(1.08)^-time period]/0.08

100,000=187,500[1-(1.08)^-time period]

(100,000/187,500)=[1-(1.08)^-time period]

[1-(1.08)^-time period] =0.533

(1.08)^-time period=1-0.533

(1/1.08)^time period=0.467

Taking log on both sides;

Time period *log (1/1.08) =log 0.467

Time period =log 0.467/log (1/1.08)

= 9.90 years.

Hence, the correct answer is 9.90 Years