Question

Consider a credit card with a balance of $8500 $ ⁢and an APR of 17.99% . In order to pay off the balance in 3 years, what monthly payment would you need to make? Round your answer to the nearest cent, if necessary.

Answer 1

Explanation:

To calculate the monthly payment needed to pay off a credit card balance in a specific time frame, we can use the formula for the monthly payment on an amortizing loan:

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

Where:

P = Principal balance (credit card balance)

r = Monthly interest rate (APR divided by 12 and converted to decimal)

n = Total number of monthly payments (number of years multiplied by 12)

Let's calculate the monthly payment for the given credit card balance and APR:

Principal balance (P) = $8500

APR = 17.99%

Monthly interest rate (r) = 17.99% / 12 / 100 = 0.0149958 (approximately)

Number of monthly payments (n) = 3 years * 12 months/year = 36

Substituting these values into the formula:

Monthly Payment = (8500 * 0.0149958 * (1 + 0.0149958)^36) / ((1 + 0.0149958)^36 - 1)

Using a calculator, the monthly payment is approximately $311.68 (rounded to the nearest cent).

Therefore, to pay off the credit card balance of $8500 in 3 years, you would need to make a monthly payment of $311.68.