Determine the cost of credit for a 2-year, $5,000 credit card loan with a monthly payment of $257.67, which corresponds to a fixed compound interest rate of 21.3% compounded monthly. Round the answer to two decimal places as needed
To determine the cost of credit for a 2-year, $5,000 credit card loan, we need to find the total amount paid back to the lender over the course of the loan. We can use the formula for the future value of an ordinary annuity:
Future Value of an ordinary annuity = Payment amount x [((1 + interest rate)^number of periods) - 1] / interest rate
Here, the payment amount is $257.67, the interest rate is 21.3% divided by 12 (since it is a monthly compound interest rate), and the number of periods is 2 years multiplied by 12 months.
Future Value = $257.67 x [((1 + 0.213/12)^(2*12)) - 1] / (0.213/12)
Future Value = $257.67 x [((1 + 0.017775)^(24)) - 1] / (0.017775)
Future Value ≈ $7,698.26
To find the cost of credit, we need to subtract the initial loan amount from the total amount paid back:
Cost of Credit = Future Value - Loan Amount
Cost of Credit = $7,698.26 - $5,000
Cost of Credit ≈ $2,698.26
Therefore, the cost of credit for this loan is approximately $2,698.26.