# How do you split capital and interest on finance agreements? Sum-of-digits

From a business perspective it makes sense to spread the cost of purchasing assets rather than using up working capital and putting pressure on your cash flow. The Matching of Revenue and Expenditure is a fundamental accounting concept.

Assets such as vehicles are often financed over 3 years, generally, the monthly payments are a fixed amount, but when the payments are posted to the Accounts, Capital needs to be posted against the Loan Balance on the Balance Sheet and Interest needs to be posted to the Profit & Loss.

There are basically two methods to calculate the split:

Simple Interest

Interest is calculated on the balance outstanding as follows Balance x Interest Rate/12 months

Here is a link to a Microsoft Template for Simple Interest

http://office.microsoft.com/en-us/templates/loan-calculator-TC006206287.aspx

Investopedia says:

The standard loan is called “simple interest”. You borrow some money and at the end of the period you pay it back plus interest. For longer term loans, you make periodic payments. With some consumer loans, especially with auto loans, you may encounter a different type of loan which mentions the “Rule of 78”. It is a different way of deciding how much of each monthly payment is interest and how much is principal.

Sum of Digits (Rule of 78’s)

The sum of digits method uses the formula:

(n x (n+1))/2

Sum-of-the-digits method, also know as the Rule of 78s is a term used in lending that refers to a method of yearly interest calculation. 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.). This is an accurate interest model only based on the assumption that the borrower pays only the amount due each month. If the borrower pays off the loan early, this method maximizes the amount paid by applying funds to interest before principal.

A 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). The denominator of a Rule of 78 loan is the sum of the digits, the sum of the number of monthly payments in the loan. For a 12 month loan, the sum of numbers from 1 to 12 is 78 (1 + 2 + 3 + . . . +12 = 78). For a 24 month loan, the denominator is 300. The sum of the numbers from 1 to n is given by the equation n * (n+1) / 2. If n were 24, the sum of the numbers from 1 to 24 is 24 * (24+1) / 2 = 12 x 25 = 300, which is the loan’s denominator, D.

http://en.wikipedia.org/wiki/Rule_of_78s

I have created a template for the Sum-of-digits method and you can download it using this link

Comparison

If you take the following example:

Asset cost £18,000

Deposit £1,800

Loan £16,200

Repayments 36 x £500

Interest Rate 6.9718%

The total interest charged over 3 years is the same £1,800 but the monthly interest is different, simple interest for month 1 = £94.12 but using sum-of-digits its £97.30. This means that with the sum of digits method the balance due for early repayment will be higher.

steve@bicknells.net