Question

Your father loans you $12,000 to make it through your senior year. His repayment schedule requires payments of $1,401.95 at the end of year for the next 15 years.

What interest rate is he charging you? A) 7.5% B) 8.0% C) 7.0% D) 8.5%

Please show work and formula used. Thank you so much!

Answer 1

This can be solved using the Present value of annuity formula

Present value of annuity is = P*(1-(1+r)^-n)/r

"P" is Annual payment = $ 1,401.95/.

Present value of annuity is = Loan = $ 12,000/.

"r" is Annual interest rate = ?

"n"is No of years = 15

12000=1401.95*(1-(1+r)^-15)/r

(1-(1+r)^-15)/r=(12000/1401.95)

(1-(1+r)^-15)/r=8.55950640

(1-(1+r)^-15)=8.55950640*r

Using trial and error method, r is = 8.00205%

Interest rate charged is = 8%

Option B)