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.

Question

Keegan

Mathematics

7 December, 19:33

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.

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Misael Valdez · 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.