600 CHAPTER 10 Consumer Mathematics A borrower may wish to pay back part of a loan prior to the due date. The next example illustrates how a partial payment is credited under the United States rule. Making partial payments reduces the amount of interest paid and thus the cost of the loan. Example 6 Loan Due Date Determine the due date of a loan made on April 7 for 180 days. Solution We will use Table 10.1 to determine the due date of the loan. In the table, first locate Day 7 in the far-left column and then move directly to the right four columns, to the April column. We can see that April 7 corresponds to the number 97, circled in red, in the table. Thus, April 7 is the 97th day of the year. Since the loan is due 180 days after April 7, we add 180 to 97. Note that 97 180 277. + = The due date is the 277th day of the year. From Table 10.1 we see that the number 277, circled in blue, corresponds to Day 4 of October. Thus, the due date of the loan is October 4. 7 Now try Exercise 35 Example 7 Loan Length in Days Mariella took out a loan on March 15 and repaid the loan, with interest, on November 18. Determine the number of days of the loan. Solution To determine the number of days from March 15 to November 18, we first note from Table 10.1 that March 15 is the 74th day of the year and that November 18 is the 322nd day of the year. The difference between 322 and 74, 322 – 74, is 248. Thus, the number of days of Mariella’s loan is 248 days. 7 Now try Exercise 39 Example 8 Using the Banker’s Rule Using the Banker’s rule, determine the simple interest that will be paid on a $2700 loan at an interest rate of 2% for the period of March 15 to November 18. Solution The principal is $2700 and the rate, written as a decimal number, is 0.02. In Example 7, we determined that the number of days from March 15 to November 18 is 248 days. Therefore, the period of time in years is . 248 360 Substituting into the simple interest formula gives i p r t $2700 0.02 248 360 $37.20 = × × = × × = Thus, the simple interest is $37.20. 7 Now try Exercise 45 Example 9 Using the United States Rule Cathy is a mathematics teacher, and she plans to attend a national teachers conference. To pay for her airfare, on November 1, 2022, she takes out a 120-day loan for $400 at an interest rate of 12.5%. Cathy uses some birthday gift money to make a partial payment of $150 on January 5, 2023. She makes a second partial payment of $100 on February 2, 2023. a) Determine the due date of the loan. b) Determine the interest and the amount credited to the principal on January 5. c) Determine the interest and the amount credited to the principal on February 2. d) Determine the amount that Cathy must pay on the due date. Carlos Enrique Santa Maria/123RF
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