Calculating Interest Rate?

In a discount interest loan, you pay the interest payment up front. For example, if a 1 yr 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 yr.


A. what is the effective interest rate on this loan?


b. if you call the discount d (for ex 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?

Calculating Interest Rate?
a.) Divide the interest paid by the amount received: 1000/9000 = 11.1% loan





b.) Use the example above. 1000 can be expressed as P (principal) * d (discount rate). 9000 can be expressed as P * (1-d). Thus,


I = P * d / P * (1-d)





I'll leave c. to you.