Jim's Electrical is offered a $400,000 line of credit for six months at an APR of 9%.The bank requires that the firm keep an amount equal to 5% of the loan principal in a non-interest-earning account with the bank as long as the loan remains outstanding.What is the actual six-month interest rate paid,expressed as an EAR?

Question

Quizplus · Accepted Answer

The actual amount borrowed by Jim's Electrical is $400,000 - (5% of $400,000) = $380,000.
The interest paid for six months at an APR of 9% is:
$380,000 x 9% x (6/12) = $17,100
To find the EAR, we use the formula:
EAR = (1 + (APR/m))^m - 1
where m is the number of compounding periods in one year.
Since the loan is for six months, there will be two compounding periods in one year.
EAR = (1 + (0.09/2))^2 - 1 = 0.097 = 9.70%
Therefore, the actual six-month interest rate paid, expressed as an EAR, is 9.70%.

Jim's Electrical Is Offered a $400,000 Line of Credit for Six