# Rule of 78

Posted by Professor Cram in Consumer Credit and Banking

## Rule of 78

The Rule of 78 is a method of allocating interest charges for the life of a loan to the periods within the loan. It was developed as a simple (but inaccurate) method for calculating interest refunds in case of early repayment of a loan. The existence of financial calculators and electronic spreadsheets with financial calculation capability renders this an archaic practice. (See Compound Interest Made Simple for an easier way to find compound interest.)

The Rule of 78 methodology also allocates a slower payoff of the loan and higher interest charges for early payoff than using outstanding balance. This method was outlawed in the U.S. in 1992 for loans longer than 5 years. Use on loans for less than 61 months is subject to state laws.

Under the Rule of 78 method, interest is calculated for the life of the loan and then allocated to each month by proportion using reverse sum of the digits methodology. You start by adding up the numbers of months for the note. For example, in a 12 month loan, counting month 1, plus month 2, and so forth through month 12 is:

- 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

This totals 78, and hence the name, rule of 78s.

The simple interest total for the loan life (as given by the formula: Interest = Rate x Time x Principal) is divided by the sum of the digits (78 in this example) and applied in reverse proportion across the life of the loan. Thus, 12/78 of the interest applies to the first month, 11/78 to the second month, and so forth down to 1/78th at the end of the 12th month.

## Example of Rule of 78

Let's look at the example of a $20,000 loan at 5% interest for 2 years. Under the Rule of 78 method, we first add up the months for the note:

- 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 = 300

Now, we calculate the simple interest total for the life of this loan:

- Interest = Rate x Time x Principal
- Interest = 5% x 2 years x $20,000
- Interest = $2,000

Finally, we divide the interest total by the sum of the digits (300) and apply in reverse proportion:

- Month #1: $2,000 x (24/300) = $160
- Month #2: $2,000 x (23/300) = $153
- Month #3: $2,000 x (22/300) = $147
- Month #4: $2,000 x (21/300) = $140
- ……..
- Month #22: $2,000 x (3/300) = $20
- Month #23: $2,000 x (2/300) = $13
- Month #24: $2,000 x (1/300) = $7

As you can see, the amount of interest in the Rule of 78 is higher in the beginning and reduces over the life of the loan.

A point for multiple choice exams - the rule of 78 does NOT refer to the year the rule was adopted or banned.

A last important lesson: the Rule of 78 doesn't need to have the number 78 in it!

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If i ask to give out the raw of mathematic is it be correct of dis?