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10. Applying the rule of 78s to determine prepayment penalties Most installment loan contracts that use the add-on method include a prepayment penalty. A prepayment penalty is a special charge assessed to the borrower for paying off a loan early. The rule of 78s method (also called the sum of the digits method) is the most widely used method for calculating a prepayment penalty. Its name . derives from the fact that for a one-year loan, the numbers between 1 and 12 representing each month add up to 78 (12 + 11 + 10 + 9 + 8 + 7+ 6 + 5 + 4 + 3 + 2 + 1 = 78). To illustrate the use of the rule of 78s method, consider the following example: : Janet Zhou from Columbus, Ohio, has borrowed $1,500 for 12 months plus an additional finance charge of $240. She is scheduled to pay equal monthly installments of $145 ($1,740 / 12). Assume that Janet wants to pay off the loan after only 3 months. Step 1: Each month of Janet's loan is assigned a value (12 for the first month, 11 for the second month, 10 for the third month, and so on). Janet has the loan for the first 3 months. Adding up the values for each of the first 3 months gives you the following number: Step 2: According to the rule of 78s method, the lender assumes that a portion of the $240 add- on interest has already been paid. To determine how much interest that Janet has already paid, divide your answer from step 1 (the sum of the values for each month that Janet has 1 ( the loan) by 78. Then multiply this ratio by the total amount of add-on interest ($240). (Note: Round your answer to the nearest cent.) Interest Paid = (C/78)

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