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.

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  a) $96.65

  b) $28,995

  c) 51.7% to principal; 48.3% to interest

Step-by-step 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.

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