Question

You have saved $44,000 for college and wish to use $12,000 per year. If you use the money as an ordinary annuity and earn 5.15% on your investment, how many years will your annuity last? Use a calculator to determine your answer.

3.59 years

3.36 years

4.17 years

4.27 years

Answer 1

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

44000=12000[1-(1.0515)^-time period]/0.0515

44000=233,009.7087[1-(1.0515)^-time period]

[1-(1.0515)^-time period]=(44000/233,009.7087)

(1/1.0515)^time period=1-(44000/233,009.7087)

Taking log on both sides;

time period*log(1/1.0515)=log 0.811167

time period=log 0.811167/log(1/1.0515)

=4.17 years(Approx).