596 CHAPTER 10 Consumer Mathematics Ordinary Interest The most common type of simple interest is called ordinary interest. When computing ordinary interest, we will use the Banker’s rule . The Banker’s rule states that a month has 30 days, a year has 12 months, and therefore, a year has 30 12 × or 360 days. When computing ordinary interest using an annual simple interest rate, if the time given is 5 months then we will use t . 5 12 = If the time given is 73 days, then we will use t . 73 360 = In this textbook, simple interest will mean ordinary interest unless stated otherwise. Did You Know? Origin of Banks In ancient Babylonia, as early as 2000 B.C ., temples were considered safe depositories for assets. It was believed that these sacred places enjoyed the special protection of the gods and were not likely to be robbed. It is no coincidence that many of the bank buildings built during the early twentieth century resembled ancient temples. In medieval times, monies were kept in vaults protected by armies of the ruling nobility. The word bank is derived from the Italian word banca , meaning “board.” It refers to the counting boards used by merchants. Dishonest moneychangers in the marketplace had their boards smashed to prevent them from continuing in business. The word bankrupt is literally “a broken (ruptured) board.” Example 1 A New Deck Zawfar needs to borrow $8500 to replace the deck at his home. From his credit union, Zawfar obtains a 30-month loan with an annual simple interest rate of 4.9% a) Calculate the simple interest he is charged on the loan. b) Determine the amount, principal plus interest, Zawfar will pay the credit union at the end of the 30 months to pay off his loan. Solution a) To determine the interest on the loan, we use the formula i prt. = We know that p $8500 = and r 4.9%, = which written as a decimal number is 0.049. The time stated was 30 months, but since we were given an annual rate, we must convert time to years. The time in years is t 2.5. 30 12 = = We substitute the appropriate values in the simple interest formula i p r t $8500 0.049 2.5 $1041.25 = × × = × × = The simple interest on $8500 at 4.9% for 30 months is $1041.25. b) The amount to be repaid is equal to the principal, $8500, plus the interest, $1041.25. A p i $8500 $1041.25 $9541.25 = + = + = To pay off his loan, Zawfar will pay the credit union $9541.25 at the end of 30 months. 7 Now try Exercise 25 Paying off debt Example 2 Determining the Annual Rate of Interest Philip agrees to lend $850 to his friend Joe to help Joe travel to Cincinnati to attend a family wedding. Nine months later, Joe repaid the original $850 plus $51 interest. What annual rate of interest did Joe pay to Philip? Solution We need to solve for the interest rate, r. Since the time is 9 months, the time in years is , 9 12 or 0.75. Using the formula i prt, = we get r r r r $51 $850 0.75 51 637.5 51 637.5 637.5 637.5 0.08 = × × = = = Divide both sides of the equation by 637.5. To change this decimal number to a percent, multiply by 100 and add a percent sign. Thus the annual rate of interest paid by Joe to Philip is 8% 7 Now try Exercise 27
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