Rule of 78 Loan

Some creditors use tables based on a method called the Rule of 78, also known as the sum of the digits method to determine how much interest you have paid at any point in a loan.

The number 78 comes from the 12 months in a one year period. The sum of those parts (1 + 2 + 3 .. + 12) is 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.

This method was initially used as an approximation of the standard installment loan amortization method. As it doesn't calculate interest on the outstanding balance but simply attributes a predetermined part of the total interest, this has the effect of decreasing the balance more slowly.

If you don't pay off the loan early, you pay the same amount of interest using standard amortization or Rule of 78 amortization. However, if you do pay off early, you will end up paying more interest with a Rule of 78 loan than with a corresponding standard installment loan. For that reason, you should avoid loans that use the Rule of 78 method.

When deciding whether or not to pay off a Rule of 78 loan early, you should know the amount of interest you'll save, you may be better off investing the funds elsewhere rather than paying off the loan.

In 1992, the U.S. Congress outlawed the use of the "Rule of 78" formula in closed-end loans longer than 61 months. Whether a lender can apply the method to installment loans of five years or less is a matter of state law. Many U.S. states prohibit the practice.

Please have a look at the example below to see the difference between the two methods.

To see the amortization schedule, select the Show Details command in the Calculation menu.

To toggle between date and year/period view, click the first column header in the Details.

To change the start date, select the Start Date command in the Edit menu to open the Date Options dialog.

Input

• nominal annual rate

• compounding frequency

• payment frequency

• number of years or payments

• present value (principal) of the loan

Results

• periodic payment

• future value

• total paid

• total interest

Example

•

A debt of $10,000 with interest at 8 % compounded monthly is to be amortized by equal monthly payments over the next four years, the first payment due in one month.

If the contract is signed on March 1st, 2004, what will be the outstanding balance on July 1st, 2005 using the standard installment loan amortization and the rule of 78 loan amortization method?

Input	Nominal annual rate:	8 %
	Interest is compounded:	monthly
	Payments are made:	monthly
	Number of payments:	48
	Present value:	10,00s0

Result	Periodic payment:	244.13

Switching between the Installment Loan and Rule of 78 Loan calculations and examining the details you'll see that:

when Rule of 78 amortization is used, the balance on July 1st, 2005 is $7,040.70.
when standard amortization is used, the balance is $7,014.11, or $26.59 less.

The $26.59 amounts to a 2.66 % penalty.

For this example, the balance that the Rule of 78 method produces is always greater than with standard amortization, the largest difference occurs around 1/3 through the loan.

Related topics

Prepaid Interest Loan

Extra Principal Payments Loan