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 785 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 785 method, consider the following example: Crystal Lalime from Reno, Nevada, has borrowed $4,500 for 12 months plus an additional finance charge of $720. She is scheduled to pay equal monthly installments of $435 ($5,220 / 12). Assume that Crystal wants to pay off the loan after only 8 months Step 1: Each month of Crystal's loan is assigned a value (12 for the first month, 11 for the second month, 10 for the third month, and so on). Crystal has the loan for the first 8 months. Adding up the values for each of the first 8 months gives you the following number: Step 2: According to the rule of 785 method, the lender assumes that a portion of the $720 add-on interest has already been paid. To determine how much interest that Crystal has already paid, divide your answer from step 1 (the sum of the values for each month that Crystal has the loan) by 78. Then multiply this ratio by the total amount of add-on interest ($720). (Note: Round your answer to the nearest cent.) Interest Paid =( /78) x $720 = $ Step 3: After months, Crystal has made a total of $3,480 in payments. Subtract the total amount of interest paid (from step 2) from $3,480. This gives you the amount of the $4,500 originally borrowed that has been repaid. Perform this calculation to determine how much of the original loan (the principal) has been repaid: (Note: Round your answer to the nearest cent.) $3,480 (Total Payments Made) - $ (Interest Paid) = $ (Amount of Original $4,500 Borrowed That Has Been Repaid) Step 4: Determine how much of the original amount borrowed remains unpaid. Subtract the amount of the principal that has been repaid (from step 3) from the original amount borrowed: (Note: Round your answer to the nearest cent.) $4,500 (Original Amount Borrowed) - $ (Amount of Principal Repaid) - $ (Principal Left Unpaid) Step 5: Crystal pays off her loan after only months, which is two-thirds (8/12 = 2/3) of the way through the loan. Crystal might (incorrectly) expect to owe only $1,500 of the original amount borrowed (the remaining third of the original amount borrowed). (Note: Round your answer to the nearest cent.) However, in reality, Crystal still owes $ of the original amount borrowed (from step 4). Now you can calculate the prepayment penalty as follows: (Amount of Original Loan Unpaid) $1,500 = $ (Prepayment Penalty)