Question

A person has 80000 in savings account that earns interest at 7.5% per year, compounded annually. If the person withdraws 12000 at the end of each year after how many years will the savings be exhausted? Ans:10 yrs

Show hand work not answer by calculator

Answer 1

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

80,000=12000[1-(1.075)^-time period]/0.075

80,000=160,000[1-(1.075)^-time period]

(80,000/160,000)=1-(1.075)^-time period

1-(80,000/160,000)=(1.075)^-time period

(1.075)^-time period=0.5

(1/1.075)^time period=0.5

Taking log on both sides;

time period*log ((1/1.075))=log 0.5

time period=log 0.5/log(1/1.075)

which is equal to

=10 years(Approx).