The Rule of 78s is a method used in accounting for asset depreciation.

Here is an example…when you purchase a car, with each year that passes, the value of that car is less.

In accounting terms, this declining value is called depreciation. There are many methods of calculating the depreciation of an asset. One method is called Straight Line and simply assumes a certain useful life, say 10 years, and for each year that passes, the asset is worth 1/10 less than it was the previous year. In our example of the car, above, if the initial value of the car was $10,000.00, after one year the car would be worth $9,000.00, after the second year $8,000.00, and so on.

Another more complex method of depreciating the value of an asset is called the Sum of the Year’s Digits Method. In this method, we add up the sum of the months (or years) which exist in the useful life of an asset, and then use this figure as the divisor, using each period’s digit as the numerator. In the above example with the car, we add up the digits of the years in the useful life of the car, 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1, and we get 55. Then, starting with the largest number, namely “10”, we divide 10 by 55 and multiply this by the initial value of the car…10 / 55 x 10,000 = $1,818.18. This figure, $1,818.18 is the amount of value that the car loses in the first year. So, after the first year, using this method, the value of the car is $8,181.82. After the second year, the car loses another 9 / 55 * 10,000, or $1,636.36 of value and is worth only $6,545.45.

So, what does all of this have to do with the Rule of 78s? By taking the sum of the year’s digits for a 12-month year, we get 12 + 11 + 10 + 9 + 8 + … + 1, you got it, 78! The Rule of 78s and the Sum of the Year’s Digits are the same thing.

Several years ago, the lawmakers that decided how premium financing was going to work decided to borrow the Rule of 78s from accounting standards for depreciation and employ them in calculating interest recognition in premium financing.

In premium financing, when a loan is first calculated (i.e. when a quote is first given and a premium finance agreement is signed), the borrower is presented with a set of terms, including among other figures, the principal amount of the loan, the number of installments in which the borrower must repay the loan, and the amount of interest to be charged.

If the borrower pays the loan off sooner than expected (which can occur by the borrower paying off the loan before the term, or if the borrower doesn’t make a payment, the loan is canceled and the insurance carrier sends in the unearned premium), the borrower is entitled to a refund of a portion of the interest (the Finance Charge) which was initially listed on the premium finance agreement. The method by which a premium finance company calculates the amount of the Finance Charge that the borrower is entitled to is often times calculated in accordance with the Rule of 78s.

**Example Loan:**

* Loan Amount: $1,000.00 *

* # of Installments: 9 *

* Interest Charge: $120.00 *

* Effective Date January 1st*

Scenario: The borrower makes 2 installments (the February and March payments), and then stops making payments. The premium finance company cancels the policy in April and the insurance carrier sends back the unearned premium in June, which pays off the entire loan balance. How much of the original $120.00 finance charge does the borrower get back?

The loan was 9 months in length, so we add up the figures from 9 to 1…this gives us 45. Using 45 as the denominator, we then add up the digits for each month, starting with the largest digit, and counting down until we reach the month during which the loan was paid off. The loan started in January and was not paid off until June. This is 6 months, so we add up the first 6 digits, starting with the largest one…9 + 8 + 7 + 6 + 5 + 4 = 39. We then calculate 39 / 45 * $120.00 = $104.00.

This is our answer! The premium finance company is permitted to keep $104.00 of the $120.00 finance charge and must refund back $16.00 to the borrower.

Written By: Todd Greenbaum