Answer:
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.
