Question

You have $90,000 in student loans with an annual payment of $10,500 and an annual interest of 7%.

A) How long would it take you to pay off the loan?B

B) What would be the annual payments should you want to pay off the loan in 10 years?

Answer 1

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

90,000=10500[1-(1.07)^-time period]/0.07

90,000=150,000[1-(1.07)^-time period]

[1-(1.07)^-time period]=(90,000/150,000)

1-(90,000/150,000)=(1/1.07)^time period

Taking log on both sides;

log 0.4=time period*log (1/1.07)

time period=log 0.4/log (1/1.07)

=13.54 years(Approx)

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

90,000=Annuity[1-(1.07)^-10]/0.07

90,000=Annuity*7.023581541

Annuity=90,000/7.023581541

=$12813.98(Approx).