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?

Answer 1

Calculating how much the son will pay, multiply the $1401.95 x 12 = $21 029.25. Then, taking $21029.25-12000= 9029.25 interest. So 9029.25/12000= 75% interest which is rather high and surprising the father would charge this much to his son unless he wanted him to see the value of money and getting the loan.

Answer 2

P = $12,000, the principal
t = 15 years, the duration of the loan
n = 12, assume monthly compounding
n*t = 12*150 = 180

Because there are 15 yearly payments of $1,401.95, the value of the loan is
A = 1401.95*15 = $21,029.25

If the interest rate is r, then
12000*(1 + r/12)¹⁸⁰ = 21029.25
(1 + r/12)¹⁸⁰ = 1.7524

Because 1/180 = 0.00556, therefore
1 + r/12 = 1.7524⁰°⁰⁰⁵⁵⁶ = 1.003121
r/12 = 0.003124
r = 0.0375 = 3.75%

Answer: The interest rate is 3.75%