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?

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%

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.