Drew just took out a loan for $1250 at an 8.4% apr, compounded monthly, to buy some new brakes for his car, and he has agreed to
make monthly payments of $46.50 to pay off the loan. if he changes his monthly payment to $71.00, how much faster would he be able to pay off the loan?
2 answers:
Paying $46.50 monthly, a financial calculator says it will take 30 months to pay off the loan.
Paying $71.00 monthly, it will take 19 months to pay off the loan.
Making the higher payment, Drew can pay off his loan 11 months sooner.
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If you solve the amortization formula for n, the number of payments, you get
... n = -log(1-(Pi/A))/log(1+i)
where P is the principal value of the loan (1250), i is the monthly interest rate (.007), A is the monthly payment (46.50 or 71.00).
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