Conway's Roofing Services is offered a $1 million line of credit for three months at an APR of 8%.The bank requires that the firm keep an amount equal to 12% of the loan principal in a non-interest-earning account with the bank as long as the loan remains outstanding.What is the actual three-month interest rate paid,expressed as an EAR?

Question

Quizplus · Accepted Answer

First, we need to calculate the dollar amount that needs to be kept in the non-interest-earning account: 
12% of $1,000,000 = $120,000

Next, we need to calculate the interest paid on the remaining $880,000: 
I = P x R x T 
I = $880,000 x 0.08 x (3/12) = $17,600

Finally, we need to calculate the effective annual rate (EAR) using the following formula: 
EAR = (1 + APR/n)^n - 1 
EAR = (1 + 0.08/4)^4 - 1 = 0.0941 or 9.41%

Therefore, the actual three-month interest rate paid, expressed as an EAR, is 9.41%.

Conway's Roofing Services Is Offered a $1 Million Line of Credit