Question

While Mary Corens was a student at the University of Tennessee, she borrowed $12,000 in student loans at an annual interest rate of 8.20%. If Mary repays $1,500 per year, how long (rounded up to the nearest year) will it take her to repay the loan?

Answer 1

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

12000=1500[1-(1.082)^-time period]/0.082

12000=18292.68293[1-(1.082)^-time period]

[1-(1.082)^-time period]=(12000/18292.68293)

(1.082)^-time period=1-(12000/18292.68293)

(1.082)^-time period=0.344

(1/1.082)^time period=0.344

Taking log on both sides;

time period*log(1/1.082)=log 0.344

time period=log 0.344/log(1/1.082)

=14 years(Approx).