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=(C\cdot(r)/(m))/(1-(1+(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=(2500\cdot(0.18)/(12))/(1-(1+(0.18)/(12))^(-4\cdot12)) \\ A=(2500\cdot0.015)/(1-(1.015)^(-48)) \\ A\approx(37.5)/(1-0.4894) \\ A\approx(37.5)/(0.5106) \\ A\approx73.44 \end{gathered}`

Answer: we have to pay $73.44 each month.