Question

Stacey has a $8,000 balance on her credit card that has an interest rate of 21%, compounded monthly.

If she decides to pay it off over 5 years with equal monthly payments, how much should each payment be?

Answer 1

To pay off a $8,000 credit card balance with a 21% annual interest rate over 5 years, the monthly payment should be approximately $197.53.

Step-by-step explanation:

To find the monthly payment, we can use the formula for the monthly payment of a loan, which is:

Monthly Payment = Principal * (Annual Interest Rate/12) * (1 + (Annual Interest Rate/12))^n / ((1 + (Annual Interest Rate/12))^n - 1)

Where:

• Principal = $8,000 (balance on the credit card)
• Annual Interest Rate = 21% (converted to a decimal = 0.21)
• n = 5 years * 12 months/year = 60 months

Plugging the values into the formula, we get:

Monthly Payment = $8,000 * (0.21/12) * (1 + (0.21/12))^60 / ((1 + (0.21/12))^60 - 1)

Simplifying the equation gives:

Monthly Payment ≈ $197.53

Therefore, Stacey should make monthly payments of approximately $197.53 to pay off her credit card debt over 5 years.

Answer 2

Stacey needs to pay $214.29 per month to clear her $8,000 credit card debt with a 21% interest rate over 5 years, considering compounding interest.

Step-by-step explanation:

To determine the monthly payment for Stacey's credit card balance of $8,000 at 21% interest rate compounded monthly over 5 years, we can use the formula for the monthly payment of an installment loan, which is P = [rPV] / [1 - (1 + r)^-n], where P is the monthly payment, r is the monthly interest rate (annual rate divided by 12), PV is the present value or principal amount of the loan, and n is the total number of payments (months).

The direct answer is that Stacey would need to pay $214.29 each month to pay off her credit card within 5 years if no additional charges are made.

This calculation accounts for the compounding interest which means that each month, the interest is calculated based on the outstanding balance including previous interest. Credit card debts can have high-interest rates, and it's important to understand how that affects the total amount payable.