Question

Consider a student loan of ​$15,000 at a fixed APR of ​6% for 25 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

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Answer:

a) $96.65

b) $28,995

c) 51.7% to principal; 48.3% to interest

Explanation:

a) The monthly payment is given by the amortization formula:

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

where P is the loan amount, r is the annual rate, and t is the number of years

Filling in the given values, we find ...

A = $15,000(0.06/12)/(1 - (1 +0.06/12)^(-12(25))) ≈ $96.65

The monthly payment is $96.65.

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b) The 300 payments total ...

$96.65 × 300 = $28,995

The total amount paid is $28,995.

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c) The percentage paid toward the principal is ...

$15,000/$28,995 × 100% ≈ 51.7%

The remainder is paid toward interest: 100% -51.7% = 48.3%

51.7% is paid toward principal, 48.3% is paid for interest.