Question

You have $2500 on a credit card that charges a 18% interest rate. If you want to pay off the credit card in 4 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?$_____each month

Answer 1

We have a principal of $2500 that has to be paid in 4 years. The payments will be monthly and all equals.

The annual interest rate is 18%.

Then, we can use the expression for an annuity that is paid monthly (m = 12, the number of superiods per year):

$A=\frac{C\cdot\frac{r}{m}}{1-(1+\frac{r}{m})^{-n\cdot m}}$

where A is the monthly payment, C is the principal ($2500), r is the interest rate (r = 0.18), m is the number of superiods per year (m = 12) and n is the number of periods related to the interest rate (n =4).

Then, we can replace and solve this as:

$\begin{gathered} A=\frac{2500\cdot\frac{0.18}{12}}{1-(1+\frac{0.18}{12})^{-4\cdot12}} \\ A=\frac{2500\cdot0.015}{1-(1.015)^{-48}} \\ A\approx\frac{37.5}{1-0.4894} \\ A\approx\frac{37.5}{0.5106} \\ A\approx73.44 \end{gathered}$

Answer: we have to pay $73.44 each month.