Question

Suppose that on January 1 you have a balance of $3,100 on a credit card whose APR is 13%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. a. The monthly payment is?b. When the card is paid off, how much will you have paid since January 1?c. What percentage of your total payment from part (b) is interest?

Answer 1

The monthly payment M of an initial balancen P, with a APR r during a period of t months is given by:

$M=P\frac{\frac{r}{12}(1+\frac{r}{12})^t}{(1+\frac{r}{12})^{12}-1}$

a) For P = $3,100, r = 13% and t = 12 months, we have:

$M=3100\frac{\frac{0.13}{12}(1+\frac{0.13}{12})^{12}}{(1+\frac{0.13}{12})^{12}-1}\approx\text{ \ }276.88$

b) The total payment after 12 months will be:

$T=12\cdot M=12\cdot276.88=\text{ \ }3322.60$

c) The total interest is given by:

$I=\frac{T}{P}-1=\frac{3322.60}{3100}-1\approx0.072=7.2\%$