Question

Consider a student loan of ​$17 comma 500 at a fixed APR of 9​% for 15 years.

a. The monthly payment is ​$_____
​(round to the nearest cent as​ needed.)

b. The total payment over the term of the loan is ​$______
​(Round to the nearest cent as​ needed.)

c. Of the total payment over the term of the​ loan, _____​% is paid toward the principal and _____​% is paid toward interest.
​(Round to the nearest tenth as​ needed.)

Answer 1

a) monthly payment: $177.50

b) total amount paid: $31,950

c) toward principal: $17,500; toward interest: $14,450

Explanation:

a) The amount of the monthly payment (A) is computed from the principal (P), the annual interest rate (r) and the number of years (n) using the formula ...

A = P·(r/12)/(1 -(1 +r/12)^(-12n))

Filling in your numbers, we can use r/12 = 0.09/12 = 0.0075, and 12n = 12·15 = 180:

A = $17500·0.0075/(1 - 1.0075^-180) ≈ $177.50

__

b) The total payment over the term of the loan is 180 of these monthly payments:

180·$177.50 = $31,950

__

c) $17,500 is paid toward the principal.

$14,450 is paid toward interest.