Question

You have $4,000 on a credit card that charges a 15% interest rate. If you want to pay off the credit card in 3 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

Answer 1

The formula to calculate the monthly payment is given to be:

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

where

$\begin{gathered} A=\text{ Monthly Payment} \\ P=\text{ }Loan\text{ amount} \\ r=\text{ }Interest\text{ rate per period} \\ n=\text{ Total number of periods} \end{gathered}$

From the question provided, we have the following parameters:

$\begin{gathered} P=4,000 \\ r=\frac{0.15}{12}=0.0125 \\ n=3\times12=36\text{ months} \end{gathered}$

Therefore, we can input these values into the formula and calculate the monthly payment as follows:

$\begin{gathered} A=4000\times\frac{0.0125\times(1+0.0125)^{36}}{(1+0.0125)^{36}-1} \\ A=138.66 \end{gathered}$

The amount to be paid monthly is $138.66