Question

You have $4,000 on a credit card that charges a 19.8% 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 else to the card during this time)?

Answer 1

To pay off a $4,000 credit card debt at a 19.8% annual interest rate in 4 years, you need to calculate the monthly payment using the annuity formula, converting the interest rate to monthly and determining the number of payments.

Step-by-step explanation:

To calculate the monthly payment needed to pay off a $4,000 credit card debt at a 19.8% annual interest rate in 4 years, you can use the formula for the monthly payment on an installment loan, which is based on the annuity formula. First, you need to convert the annual interest rate to a monthly rate by dividing by 12.

The monthly interest rate is 19.8% / 12, which equals 1.65%. Next, you must calculate the number of monthly payments, which is 4 years × 12 months/year = 48 payments.

Using the annuity formula:

Monthly Payment = P × [r(1+r)^n] / [(1+r)^n – 1],

where:

• P is the principal amount ($4,000)
• r is the monthly interest rate (0.0198/12)
• n is the total number of payments (48)

By substituting the values into the formula and solving for the monthly payment, you would find the required monthly payment to pay off the credit card in 4 years.

It is important to note that this formula assumes no additional charges on the credit card and that the payments are made regularly on a monthly basis without fail.