Question

Consider a student loan of ​$22,500 at a fixed APR of 6​% for 20 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.

Answer 1

a) For principal amount P, interest rate r, and number of years t, the amortization formula for the monthly payment A is ...

... A = P(r/12)/(1 -(1 +r/12)^(-12t))

... A = 22500·(0.06/12)/(1 -(1 +0.06/12)^(-12·20)) ≈ 161.20

The monthly payment is $161.20.

b) After 240 payments, the amount repaid is

... $161.20·240 = $38,688

c) (22500/38688)·100% = 58.2% is paid toward principal

The remaining amount, 41.8% is paid toward interest.