Question

You just invested $50,000 into an account that earns 7 percent compounded annually. At the end of each year you can withdraw $4,971. How many years can you continue to make the withdrawals ?

a. 12

b.13.5

c.18

d.10

Answer 1

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

50,000=4,971[1-(1.07)^-time period]/0.07

50,000=71014.28571[1-(1.07)^-time period]

50,000/71014.28571=[1-(1.07)^-time period]

(1.07)^-time period=1-(50,000/71014.28571)

(1/1.07)^time period=0.295916314

Taking log on both sides;

time period*log(1/1.07)=log 0.295916314

time period=log 0.295916314/log(1/1.07)

=18 years.