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4.D.15 Consider a student loan of $17,500 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 a. The monthly payment is $ (Do not round until the final answer. Then round to the nearest cent as needed.) ess ibrary

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sqdancefan

Answer:

  a.  $112.75

  b.  $33,825.82

  c.  principal: 51.7%; interest: 48.3%

Step-by-step explanation:

a. The loan amortization formula tells you the monthly payment is ...

  A = P(r/n)/(1- (1+r/n)^(-nt))

for a loan of principal P at interest rate r compounded n times per year for t years. Filling in the given numbers, we get ...

  A = $17,500(.06/12)/(1 -(1+.06/12)^(-12·25)) ≈ $112.752745

The monthly loan payment will be $112.75.

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b. The amount paid over the term of the loan is ...

  (25 yr)(12 mo/yr)($112.752745/mo) = $33,825.82 . . . . total amount repaid

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c. The amount of that going to the principal is ...

  17,500/33,825.82 ≈ 51.736% . . . . fraction to principal

The remaining amount, 48.264% goes to interest.

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Comment on cents

If you multiply the (rounded) monthly payment by the number of payments, the amount repaid comes to $33,825.00. The 82 cents extra comes from the fact that the payment is actually rounded down from the amount computed, so the amount due for the final payment will make up the difference. The amount due on a loan in the real world may depend on the way rounding is done in the loan calculations over the 25-year life of the loan. A spreadsheet can show the effects of different rounding scenarios. (In general, the amount of the final loan payment is different from the others.)

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