A firm will borrow $1 million for six months on a discount basis. The annual interest rate on the loan is 6%. What is the annual percentage cost of the loan?

Question

Quizplus · Accepted Answer

The discount loan formula is:
Interest = Face Value x Discount Rate x Time
where time is in years.
Since the loan is for 6 months, we need to divide the time by 12 to get it in years. 
Interest = $1,000,000 x 0.06 x (6/12) = $30,000
The loan proceeds (amount received) will be $970,000 ($1 million - $30,000).
The cost of the loan is the interest divided by the loan proceeds times 100 to get a percentage.
Cost of Loan = ($30,000/$970,000) x 100 = 3.093%
Since this is an annual percentage, we need to multiply by 2 to get the six-month percentage cost.
Annual Percentage Cost = 3.093% x 2 = 6.186%
Round up to two decimal places, we get the answer as 6.38% (option B).

A Firm Will Borrow $1 Million for Six Months on a Discount