The Rule of 78's
The "RULE OF 78’S" method of computing refunds, which is also referred to as the "Sum of Digits" method, primarily applies to transactions: (1) Repayable in equal monthly installments, and (2) where the debt or amount owed is expressed as a single sum comprised of the amount financed and the finance charge computed in advance.
EXAMPLE:
Amount Financed | $1,000.00 |
Finance Charge Computed in Advance | $ 90.44 |
Amount Owed (Total of Payments) | $1,090.44 |
Repayable in 12 monthly installments of $90.87 each | |
Annual Percentage Rate is 16.29% |
The following table shows how the "Rule of 78’s" or "Sum of Digits" method applies to the above transaction:
INSTALLMENTS | (1) NUMBER OF DIGITS |
(2) EARNED FINANCE CHARGE | (3) UNEARNED FINANCE CHARGE |
---|---|---|---|
1^{ST} |
12 |
12/78 of $90.44=$13.91 | 66/78 of $90.44=$76.53 |
2^{ND} |
11 |
23/78 of $90.44=$26.67 | 55/78 of $90.44=$63.77 |
3^{RD} |
10 |
33/78 of $90.44=$38.26 | 45/78 of $90.44=$52.18 |
4^{TH} |
9 |
42/78 of $90.44=$48.70 | 36/78 of $90.44=$41.74 |
5^{TH} |
8 |
50/78 of $90.44=$57.97 | 28/78 of $90.44=$32.47 |
6^{TH} |
7 |
57/78 of $90.44=$66.09 | 21/78 of $90.44=$24.35 |
7^{TH} |
6 |
63/78 of $90.44=$73.05 | 15/78 of $90.44=$17.39 |
8^{TH} |
5 |
68/78 of $90.44=$78.85 | 10/78 of $90.44=$11.59 |
9^{TH} |
4 |
72/78 of $90.44=$83.48 | 6/78 of $90.44=$ 6.96 |
10^{TH} |
3 |
75/78 of $90.44=$86.96 | 3/78 of $90.44=$ 3.48 |
11^{TH} |
2 |
77/78 of $90.44=$89.28 | 1/78 of $90.44=$ 1.16 |
12^{TH} |
1 |
78/78 of $90.44=$90.44 | 0/78 of $90.44=$ 0.00 |
(1) NUMBER OF DIGITS refers to the number of installments outstanding and to the number of digits which are applicable to the balance outstanding for each month.
(2) EARNED FINANCE CHARGE refers to the accumulated number of digits which are earned at the end of each month over the total number of digits applicable to the term of the transaction and the accumulated finance charge earned at the end of each month.
(3) UNEARNED FINANCE CHARGE refers to the accumulated number of digits which are unearned at the end of each month over the total number of digits applicable to the term of the transaction and the accumulated finance charge unearned at the end of each month.
The reference to the "Rule of 78’s" originates because the sum of the digits, 12 through 1 inclusive, set forth in (1) is 78.
If the account was paid in full at the end of the first month, the lender earns the amount of the finance charge applicable to the first month or to the first installment. The number of the digits applicable to the first installment is 12 and the sum of the digits applicable to the 12 installments is 78. Therefore, the lender earns 12/78^{ ths} of the finance charge, or $13.91. The sum of the digits applicable to the remaining installments is 66 (11 + 10 + 9 through 1 inclusive), therefore, the amount of the finance charge that is unearned (refund) is 66/78^{ths }of the finance charge, or $76.53.
If the account was paid in full at the end of the 11^{th} month, the lender earns the amount of the finance charge applicable to the 1^{st} through 11^{th} installment inclusive. The sum of the digits applicable to the 1^{st} through the 11^{th} installments is 77 (12 + 11 through 2 inclusive) and since the sum of the digits applicable to the 12 installments is 78, the lender earns 77/78^{ths} of the finance charge, or $89.28. The number of digits applicable to the 12^{th} installment is, therefore, the amount of the finance charge which is unearned (refund) is 1/78^{th} of the finance charge, or $1.16.
On transactions scheduled to be repaid in equal monthly installments having a term of less than 12 months, the sum of the digits will be less than 78. EXAMPLE: A 6-month transaction has a total of 21 digits, the sum of 6 through 1 inclusive. On transactions scheduled to be repaid in equal monthly installments having a term of more than 12 months, the sum of the digits will be more than 78. EXAMPLE: A 36-month transaction has a total of 666 digits, the sum of 36 through 1 inclusive.
As a general rule the percentage of the finance charge earned by a lender on transactions scheduled to be repaid in equal monthly installments will be approximately 43% if the account was paid in full at the time it was in effect for ¼ of the scheduled number of months (3 of 12, 6 of 24 or 9 of 36), and approximately 74% if the account was paid in full at the time it was in effect for ½ of the scheduled number of months (6 of 12, 12 of 24 or 18 of 36).
Making payments before they are due does not reduce the total interest owed. Only when you pay off the entire loan early will you save interest. Keep in mind that paying off a loan in, say, 15 months instead of 30 as originally planned will not produce a savings of one-half of the interest. The same is true to premiums for credit insurance, if such coverage is included on your account.
Department of Financial Institutions
Wisconsin Consumer Act Section
PO Box 8041
Madison WI 53708-8041