Calculating the Rule of 78s: Add-Ons and Simple
December 14, 2012
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.
A Rule of 78s loan employs a method of allocating the interest charge on a loan across its payment periods. As we all know, when paying off a loan, the repayments consist of two parts: the principal and the interest charge. The number 78 is derived from the 12 months in a one-year period. The sum of those parts (1 + 2 + 3 + 4 ... + 12) equals 78. 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.
Difference Between Rule of 78s and Simple
In brief, the Rule of 78 weights earlier payments with more interest than later ones. If the loan is not terminated or prepaid early, the total interest paid between simple interest and the Rule of 78 will be equal. 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. Here is an example of calculations between simple interest and Rule of 78's.
There are two kinds of rule of 78s loans: Add-on and Simple
An 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). 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. 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.
So that brings us to Rule of 78s-Simple. 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. The loan system simply sets up a simple interest loan with the same parameters in memory and runs the amortization schedule. 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. This number would be considerably lower than what you would get from the add-on interest calculation at the same rate. 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.