Final answer:
To calculate the monthly payment to pay off a $5,498 credit card debt with a 26.99% interest rate over 5 years, one must convert the annual rate to a monthly rate, then use the annuity payment formula, considering the total number of payments. The result is the monthly payment amount to clear the debt in 5 years, assuming no additional purchases are made.
Step-by-step explanation:
To determine the monthly payment required to pay off the credit card debt of $5,498 with a 26.99% interest rate compounded monthly over 5 years, we need to use the formula for calculating the monthly payment on an installment loan. The formula takes into account the principal amount, the monthly interest rate, and the total number of payments.
First, convert the annual interest rate to a monthly rate by dividing by 12:
Monthly interest rate = 26.99% / 12 months = 2.2492% per month
Next, we convert the monthly interest rate into a decimal for the calculations:
Monthly interest rate (decimal) = 2.2492% / 100 = 0.022492
We then use the annuity payment formula, which is:
Payment = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
P = principal amount ($5,498)
r = monthly interest rate (0.022492)
n = total number of payments (60 months, since we’re assuming a 5-year payoff period)
Inserting the values and calculating gives us the monthly payment amount, which is the amount the cardholder should pay monthly to clear the debt in 5 years. Since the calculation may involve many decimal places, rounding to the nearest penny is standard practice for financial calculations.
It is important to note that if any additional purchases are made on the card, or if there are other fees and charges, this will affect the monthly payment required to pay off the balance within the specified time frame.