You are considering a one-year loan of $13,000. The interest rate is quoted on a discount basis (see the previous problem) as 16 percent. What is the effective annual rate?

Data from Problem 60

This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $20,000 for one year. The interest rate is 11 percent. You and the lender agree that the interest on the loan will be .11 × $20,000  = $2,200. So the lender deducts this interest amount from the loan up front and gives you $17,800. In this case, we say that the discount is $2,200. What’s wrong here?