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(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=(0.15)/(12)=0.0125 \\ n=3*12=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*(0.0125*(1+0.0125)^(36))/((1+0.0125)^(36)-1) \\ A=138.66 \end{gathered}`

The amount to be paid monthly is $138.66