10.2 Personal Loans and Simple Interest 601 Note that in Example 9(b), if the partial payment of $150 made on January 5 had been the only partial payment made, then the balance due on March 1, 2023, would be calculated by determining the interest on the balance, $259.03, for the remainder of the loan, 55 days, and adding this interest to the principal of $259.03. If this payment had been the only partial payment made, then the balance due on March 1 would be Balance due principal interest 259.03 259.03 0.125 55 360 259.03 4.95 263.98 = + ≈ + × × ⎛ ⎝⎜ ⎞ ⎠⎟ ≈ + ≈ Solution a) Using Table 10.1, we see that November 1 is the 305th day of the year. Next, we note that the sum of 305 and 120 is 425. Since this due date will extend into the next year, we subtract 365 from 425 to get 60. From Table 10.1, we see that the 60th day of the year is March 1. Therefore, the loan due date is March 1, 2023. Had 2023 been a leap year, the due date would have been February 29, 2023. b) Using Table 10.1, January 5 is the 5th day of the year and November 1 is the 305th day of the year. The number of days from November 1 to January 5 can be computed as follows: (365 305) 5 65. − + = Then, using i prt = and the Banker’s rule, we get i $400 0.125 65 360 $9.03 = × × ≈ The interest of $9.03 that is due January 5, 2023, is deducted from the payment of $150. The remaining payment of $150 $9.03, − or $140.97, is then credited to the principal. Therefore, the adjusted principal is now $400 $140.97, − or $259.03. c) Since there was a second partial payment made, we use the Banker’s rule to calculate the interest on the unpaid principal for the period from January 5 to February 2. According to Table 10.1, the number of days from January 5 to February 2 is 33 5, − or 28 days. i $259.03 0.125 28 360 $2.52 = × × ≈ The interest of $2.52 that is due February 2, 2023, is deducted from the payment of $100. The remaining payment of $100 $2.52, − or $97.48, is then credited to the principal. Therefore, the new adjusted principal is now $259.03 $97.48, − or $161.55. d) The due date of the loan is March 1. Using Table 10.1, we see that there are 60 33, − or 27, days from February 2 to March 1. The interest is computed on the remaining balance of $161.51 by using the simple interest formula. i $161.55 0.125 27 360 = × × $1.51 ≈ Therefore, the balance due on the maturity date of the loan is the sum of the principal and the interest, $161.55 $1.51, + or $163.06. Note: The sum of the days in the three calculations, 65 28 27, + + equals the total number of days in the loan, 120. 7 Now try Exercise 59 Learning Catalytics Keyword: Angel-SOM-10.2 (See Preface for additional details.) Instructor Resources for Section 10.2 in MyLab Math • Objective-Level Videos 10.2 • Animation: Paying off Debt • PowerPoint Lecture Slides 10.2 • MyLab Exercises and Assignments 10.2
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