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.(1 point)

Question

The cost of credit is $
.
Remaining Attempts : 3

Answer 1

To determine the cost of credit for a credit card loan, we can start by calculating the total amount paid over the life of the loan and then subtract the principal amount to find the cost of credit.

1. Total Amount Paid: Calculate the total amount paid over the life of the loan:

   \[ \text{Total Amount Paid} = \text{Monthly Payment} \times \text{Number of Payments} \]

   Since the loan term is 2 years and payments are made monthly, the number of payments is:

   \[ \text{Number of Payments} = 2 \text{ years} \times 12 \text{ months/year} = 24 \text{ months} \]

   Therefore:

   \[ \text{Total Amount Paid} = 257.67 \text{ USD/month} \times 24 \text{ months} = 6,184.08 \text{ USD} \]

2. Principal Amount: The principal amount is the original loan amount, which is $5,000.

3. Cost of Credit: The cost of credit is the difference between the total amount paid and the principal amount:

   \[ \text{Cost of Credit} = \text{Total Amount Paid} - \text{Principal} \]

   Substituting the values we calculated:

   \[ \text{Cost of Credit} = 6,184.08 \text{ USD} - 5,000 \text{ USD} = 1,184.08 \text{ USD} \]

Therefore, the cost of credit is \(\boxed{1,184.08}\) USD.