The sum of the numbers from 1 to n is given by the equation n * (n+1) / 2. For a 24-month loan, the denominator is 300. For a twelve-month loan, the sum of numbers from 1 to 12 is 78 (1 + 2 + 3 +. The denominator of a Rule of 78s loan is the sum of the integers between 1 and n, inclusive, where n is the number of payments. Ī simple fraction (as with 12/78) consists of a numerator (the top number, 12 in the example) and a denominator (the bottom number, 78 in the example). That means if you pay off the loan early, you’ll end up paying more overall for a Rule of 78s loan compared with a simple-interest loan. But because of some mathematical quirks, you end up paying a greater share of the interest upfront. The Rule of 78 is designed so that borrowers pay the same interest charges over the life of a loan as they would with a loan that uses the simple interest method. If the borrower pays off the loan early, this method maximizes the interest paid by applying funds to the interest before principal. As such, the borrower pays a larger part of the total interest earlier in the term. The outcome is that more of the interest is apportioned to the first part or early repayments than the later repayments. This is an accurate interest model only based on the assumption that the borrower pays only the amount due each month. The name comes from the total number of months' interest that is being calculated in a year (the first month is 1 month's interest, whereas the second month contains 2 months' interest, etc.). Contact our sales department here to learn more.Also known as the "Sum of the Digits" method, the Rule of 78s is a term used in lending that refers to a method of yearly interest calculation. Our loan servicing software handles Rule of 78s loans with ease along with other interest types and options. So, over the life of the loan, the total yield of interest is identical to what you would get on a simple interest loan with the same parameters, but the Rule of 78s amortization will front-load that interest. This number would be considerably lower than what you would get from the add-on interest calculation at the same rate. The total interest payments over the life of that simple interest loan is then taken to be the add-on interest in the Rule of 78s calculation. The loan system simply sets up a simple interest loan with the same parameters in memory and runs the amortization schedule. If you are operating in a situation where add-on interest is not an option, then you can define the loan as Rule of 78s-Simple. Similar to the one-year loan example used above, the rule of 78s is used to determine what fraction of this add-on interest is to be paid in the first month of the loan, what fraction in the second month, etc. This resulting interest figure is added on to the principal balance of the loan, and then the result is divided by the number of payments in the loan to determine the monthly payment amount. There are two kinds of rule of 78s loans: Add-on and Simple Add-OnĪn Add-on interest loan is one where the monthly payment amount is calculated similar to what we noted above, by multiplying the principal balance by the add-on rate and then multiplying by the term (in years). Here is an example of calculations between simple interest and Rule of 78's. However, because the Rule of 78 weights the earlier payments with more interest than a simple interest method, paying off a loan early will result in the borrower paying more interest overall. If the loan is not terminated or prepaid early, the total interest paid between simple interest and the Rule of 78 will be equal. In brief, the Rule of 78 weights earlier payments with more interest than later ones. Thus, for a one-year loan 12/78ths of the interest is considered earned in month one, 11/78ths in month two and so on down to 1/78th in month twelve.ĭifference Between Rule of 78s and Simple The number 78 is derived from the 12 months in a one-year period. As we all know, when paying off a loan, the repayments consist of two parts: the principal and the interest charge. The Rule of 78s is a method for amortizing an amount of interest which has been pre-computed over the life of the loan and dividing that interest over the payments of that loan.Ī Rule of 78s loan employs a method of allocating the interest charge on a loan across its payment periods.
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