Yvonne bought a new computer and printer for college. The total cost was 2500, which she put on her new credit card that has an interest rate of 13.5%. She makes a $75.00 monthly payment. How many months will it take to pay off the credit card balance? Enter your answer as a whole number such as: 23.

  43 months

Step-by-step explanation:

The amortization formula is ...

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

We want to find the value of t for monthly payment A, financed amount P, interest rate r, and compounding monthly (n=12). Filling in the values, we have ...

  75 = 2500(0.135/12)/(1 -(1 +0.135/12)^(-12t))

  1 -(1.01125^(-12t) = 2500·0.135/(12·75) = 0.375

  1 -0.375 = 1.01125^(-12t) . . . . . add 1.01125^(-12t) -0.375

Next, take logarithms and divide by the coefficient of t.

  log(0.625)/(-12log(1.01125)) = t ≈ 3.50106 . . . . years

In months, that is ...

  3.50106×12 ≈ 42.01

The balance will be not quite zero after 42 payments. (It will be about $0.94.) It will take 43 payments to pay off the credit card balance.

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