598 CHAPTER 10 Consumer Mathematics Discount Notes In Examples 1– 4, we illustrated simple interest loans for which the interest and principal were paid on the maturity date of the loan. With a discount note, the interest on the loan is paid at the time the borrower receives the loan. This interest is called the bank discount and is deducted from the principal that the borrower receives. For example, suppose Cali receives a $1000 discount note and is charged a bank discount of $20. When Cali receives the loan, the amount of principal she receives is − $1000 $20, or $980. When Cali pays off the loan, she will pay the lender $1000. As our next example illustrates, the U.S. government uses discount notes called Treasury bills to borrow money. Example 5 U.S. Treasury Bills When an investor purchases a Treasury bill, the investor is lending money to the U.S. government. The purchase price is the face value of the Treasury bill minus the interest paid by the U.S. government on the maturity date. On February 1, Lakshmi purchased a 26-week, U.S. Treasury bill with a face value of $5000 with a bank discount of 4.65%. On the maturity date, Lakshmi will receive $5000. a) How much interest did the U.S. government pay on the maturity date? b) What is the purchase price of the Treasury bill? c) What is the actual rate of interest of the Treasury bill? Solution a) To calculate the interest, we will use the simple interest formula with p r $5000, 0.0465, = = and t 0.5. 26 52 = = i prt $5000 0.0465 0.5 $116.25 = = × × = Thus, the interest paid on the maturity date of the Treasury bill is $116.25. b) The purchase price is the face value of the Treasury bill minus the interest calculated in part a). The purchase price is − $5000 $116.25, or $4883.75. c) The actual rate of interest is calculated using the simple interest formula, with i $116.25, = and t 0.5, = from part a), p $4883.75, = from part b) i prt r r r r 116.25 4883.75 0.5 116.25 2441.875 116.25 2441.875 0.0476 = = × × = = ≈ Thus, the actual rate of interest is about 4.76%. 7 Now try Exercise 33 The United States Rule It is possible to make payments on a loan before the maturity date. A payment that is less than the full amount owed and made prior to the due date is known as a partial payment. A Supreme Court decision specified the method by which these payments are credited. The procedure is called the United States rule. The United States rule states that if a partial payment is made on the loan, interest is computed on the principal from the first day of the loan until the date of the partial payment. The partial payment is used to pay the interest first; then the rest of the payment is used to reduce the principal. Borrowers can make as many partial payments as they wish; the procedure is repeated for each payment. The balance due on
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