Question

Craig borrows $18,775 for 98 days at 10.3% exact interest, and pays an application fee of $136. Find the

effective rate (APR). (Use percent form with two decimal places in your answer.)

Answer 1

To find the effective annual percentage rate (APR), you need to consider both the interest on the loan and the application fee. After calculation, the effective APR is 3.47%.

Step-by-step explanation:

To find the effective annual percentage rate (APR), we need to consider both the interest on the loan and the application fee.

First, let's calculate the interest on the loan.

Multiply the principal ($18,775) by the interest rate (10.3%) and divide by 365 (number of days in a year) to get the daily interest rate.

Multiply the daily interest rate by the number of days (98) to get the interest on the loan.

Next, add the interest on the loan and the application fee to get the total cost.

Finally, divide the total cost by the principal and multiply by 100 to get the effective APR.

Step 1: Daily interest rate = (Principal * Interest rate) / 365

Step 2: Interest on the loan = Daily interest rate * Number of days

Step 3: Total cost = Interest on the loan + Application fee

Step 4: Effective APR = (Total cost / Principal) * 100

Plug in the values to calculate:

Daily interest rate = ($18,775 * 0.103) / 365 = $5.266

Interest on the loan = $5.266 * 98 = $515.268

Total cost = $515.268 + $136 = $651.268

Effective APR = ($651.268 / $18,775) * 100 = 3.47%