Questions: You have 2,000 on a credit card that charges a 23% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? each month

You have 2,000 on a credit card that charges a 23% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
each month

Transcript text: You have $\$ 2,000$ on a credit card that charges a $23 \%$ interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? \$ $\square$ each month Question Help: Widee Submit Question

Solution

Solution Steps

Step 1: Convert the annual interest rate to a monthly interest rate

The annual interest rate of 0.23 is converted to a monthly interest rate by dividing by 12. This gives us a monthly interest rate of 0.0192.

Step 2: Convert the repayment period from years to months

The repayment period of 5 years is converted to months by multiplying by 12. This gives us a total of 60 payments.

Step 3: Calculate the monthly payment

Using the formula $M = P \times \frac{r/12}{1 - (1 + r/12)^{-n}}$, where $P$ is the principal amount of 2000, $r/12$ is the monthly interest rate, and $n$ is the total number of payments, we calculate the monthly payment to be 56.38.