Crimini Foods is offered a $400,000 line of credit for six months at an APR of 10%. This loan has a loan origination fee of 2%. What is the actual six-month interest rate paid, expressed as an EAR
10.06%
To find the actual six-month interest rate paid, expressed as an Effective Annual Rate (EAR), we need to account for both the APR (Annual Percentage Rate) and the loan origination fee.
First, let's calculate the fee amount by multiplying the loan amount by the loan origination fee percentage.
Loan origination fee = Loan amount * Loan origination fee percentage
= $400,000 * 0.02
= $8,000
Next, we need to calculate the interest paid for six months. The APR of 10% is an annual rate, so we divide it by 12 to get the monthly rate.
Monthly interest rate = APR / 12
= 0.10 / 12
= 0.008333 (approximately)
Now, we can calculate the interest paid over six months by multiplying the monthly rate by the loan amount.
Interest paid for six months = Monthly interest rate * Loan amount * Loan duration in months
= 0.008333 * $400,000 * 6
= $19,999.20 (approximately)
Finally, we need to add the interest paid and the loan origination fee together to find the total cost of the loan.
Total cost of the loan = Interest paid for six months + Loan origination fee
= $19,999.20 + $8,000
= $27,999.20
To express this as an EAR, we need to calculate the annualized interest rate. We divide the total cost of the loan by the loan amount and then multiply by the number of times the loan is compounded in a year.
EAR = (Total cost of the loan / Loan amount) * (1 / Loan duration in months) * (Number of compounding periods in a year)
= ($27,999.20 / $400,000) * (1 / 6) * 2
= 0.069998 * 0.166667 * 2
= 0.023332 * 2
= 0.046665 (approximately)
Therefore, the actual six-month interest rate paid, expressed as an EAR, is approximately 4.67%.