Question

You have $3,000 on a credit card that charges a 19% 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)? Round to the nearest cent, do not include the dollar sign.

Answer 1

To pay off a $3,000 credit card debt at a 19% annual interest rate in 5 years, you will need to make a monthly payment of approximately $78.02, calculated using the formula for an amortizing loan.

Step-by-step explanation:

To calculate the monthly payment needed to pay off a $3,000 credit card debt at an annual interest rate of 19% over 5 years (60 months), you can use the formula for an amortizing loan which takes into account the interest rate and the number of payments. The formula for the monthly payment M is derived from the annuity formula:

M = P * (r(1+r)^n) / ((1+r)^n - 1)

Where:

• P is the principal amount ($3,000)
• r is the monthly interest rate (annual rate divided by 12 months)
• n is the total number of payments (number of years multiplied by 12)

First, convert the annual interest rate to a monthly rate by dividing by 12:

Monthly rate = 19% / 12 = 0.019 / 12 ≈ 0.001583

Plugging the values into the formula gives us:

M = 3000 * (0.001583 * (1+0.001583)^60) / ((1+0.001583)^60 - 1)

Calculating the above expression will give us the monthly payment amount. After computation, rounding to the nearest cent, you will find the monthly payment is approximately $78.02.