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
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.
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