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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<em>Comment on cents</em>
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.)
