In a discount interest loan, you pay the interest payment up front. For example, if a 1 year loan is stated as $10,000 and the interest rate is 10%, the borrower “pays” .10 × $10,000 = $1,000 immediately, thereby receiving net funds of $9,000 and repaying $10,000 in a year. (L06)
a. What is the effective interest rate on this loan?
b. If you call the discount d (for example, d = 10% using our numbers), express the effective annual rate on the loan as a function of d.
c. Why is the effective annual rate always greater than the stated rate d?