﻿ DFI: What is the Rule of 78s?

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## DFI > Education > Education Information > Consumer Credit in Indiana > What is the Rule of 78s?What is the Rule of 78s?

It's difficult to understand; yet nearly all financial institutions use it. In Indiana and other states, it is a method of figuring your cost and refund o finance charges on a precomputed credit transaction. A "precomputed" account is one which the account balance includes the finance charge and each month the full payment is subtracted from the balance. If the account pays off before maturity, a rebate of the unearned finance charge is given based on a method called "the Rule of 78s."

The Rule of 78s is commonly, even widely, used but is understood by very few people. It is a method of refunding finance charges and credit insurance premiums in some states on consumer credit precomputed transactions when the borrower prepays the account in full. More interest and insurance premiums are earned in the early stages of a contract since the amount owing is greater. As the balance decreases, the earned charges are proportionately less for each unit period.

The Rule of 78s is also known as the sum of the digits. In fact, the 78 is a sum of the digits of the months in a year: 1 plus 2 plus 3 plus 4, etc., to 12, equals 78. Under the rule, each month in the contract is assigned a value which is exactly the reverse of its occurrence in the contract. Hence, the 1st month of a 12 month contract gets the value of 12, the second month 11, etc., until the 12th month gets a value of 1. As the months elapse, the interest is earned by the lender equal to the total value of the expired months.

For example, prepaying after 2 months of a 12 month contract would result in the lender being able to keep 29.48% of the finance charges (1st month 12 plus 2nd month 11 = 23/78 or 29.48%). In another example, if the borrower prepays after 6 months, the lender would have earned 57/78s or 73.08% of the finance charges.

### Example of Rule of 78s

12 Month Loan - Made December 1 - First Payment on January 1

# Month Earned Units Unearned Units % Rebate
12 Jan 12/78 66/78 84.62%
11 Feb 23/78 55/78 70.52%
10 March 33/78 45/78 57.69%
9 April 42/78 36/78 46.15%
8 May 50/78 28/78 35.90%
7 June 57/78 21/78 26.92%
6 July 63/78 15/78 19.23%
5 Aug 68/78 10/78 12.82%
4 Sept 72/78 6/78 07.69%
3 Oct 75/78 3/78 03.85%
2 Nov 77/78 1/78 01.28%
1 Dec 78/78 0/78 00.00%
78

### Finance Charge Refund

Example:

If the finance charge on a 12 month precomputed consumer credit transaction is \$100.00 and the account is paid-in-full in the 3rd month; the total of the 1st, 2nd, and 3rd monthly earned units is 33/78 and the total unearned units is 45/78 (78 - 33). 45/78 converted to a percent is 57.69%. The unearned finance charge refund would be 57.69% of the \$100.00 finance charge which would be \$57.69.

As you can see in this example, 42.31% of the finance charge was earned in the first three months of the 12 month contract.

In Indiana under the Rule of 78s, a full month's interest can be earned during the first month of the contract and after one day into the next month. In the example given, if the account was paid in full after February 2 and on or before March 1 the refund would be \$57.69. If the account was paid-in-full March 2, the refund would be \$46.15.

If you have a precomputed account that you desire to prepay in full, always be sure to pay the account off directly before or on the date it is due. A pay-off one or a few days after the due date may cost you another month's finance charge.

### Example of a Rule of 78s

The following formula is the simplest method of computing the refunds by the Rule of 78s.

Formula

(U * (U + 1)) \ (T * (T + 1)) = Rule of 78s refund decimal * F = Rebate

 U = Unearned term periods \ = Divided by T = Term periods * = Times F = Finance Charge

Example:

This example is for a 12 month contract which prepaid at 3 months (9 months unearned) with a finance charge of \$100.00.

 U = 9 T = 12 F = \$100.00

(9 * (9 + 1)) \ (12 (12 + 1)) = (9 * 10) \ (12 * 13) = 90 \ 156 = .5769 Rule of 78s refund decimal,

.5769 * \$100.00 = \$57.69 Refund

Charts and other calculating devices are available to creditors for accurately computing the unearned charges under the Rule of 78s. You as a consumer are thus provided with an equitable refund when you prepay your obligation.

### Terms Over 61 Months

Since July 1, 1992 the Rule of 78s refund can not be used in Indiana on contracts with a term over 61 months. Refunds are computed by applying the disclosed annual percentage rate to the unpaid balances of the amount financed for the full computational periods following the prepayment, as originally scheduled or as deferred.

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