Questions: You have 4,000 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

You have 4,000 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

Transcript text: You have $\$ 4,000$ 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)? \$ $\square$ each month

Solution

Solution Steps

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

The annual interest rate of 18% is converted to a monthly rate by dividing by 12. Monthly interest rate = 18/12 = 1.5%

Step 2: Calculate the total number of payments

The total number of payments over 4 years is 4 * 12 = 48 payments.

Step 3: Apply the formula to calculate the monthly payment

The formula used is: $$M = P \times \frac{r/12}{1 - (1 + r/12)^{-n}}$$ Where:

$P$ is the principal amount = $4000
$r/12$ is the monthly interest rate = 1.5%
$n$ is the total number of payments = 48 Substituting the values into the formula, we get the monthly payment: $117.5

Final Answer:

The monthly payment required to pay off the debt is $117.5.

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