Rule of 78s
Encyclopedia
Also known as the sum-of-the-digits method, 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.
For a 12 month loan, 12/78s of the finance charge
is assessed as the first month’s portion of the finance charge, 11/78s of the finance charge is assessed as the second month’s portion of the finance charge and so on until the 12th month at which time 1/78s of the finance charge is assessed as that month’s portion of the finance charge. Following the same pattern, 24/300 of the finance charge is assessed as the first month’s portion of a 24 month precomputed loan.
Formula for calculating the unearned interest:
u = f * k(k+1)/n(n+1) u = unearned interest; f = total agreed finance charges; k = number of months paying off early; n = total term of loan in months
in 1935. Most loans in 1935 were for small amounts at low interest rates for short periods of time. It reduced the cost of loan calculations in a pre-computer era and was well suited for the small, short, and low interest rate loans of the era.
In the United States, the use of the Rule of 78s is prohibited in connection with mortgage refinancings and other consumer loans having a term exceeding 61 months.
On March 15, 2001, in the U.S. 107th Congress
, U.S. Rep. John LaFalce
(D-NY 29
), introduced H.R. 1054, a bill to eliminate the use of the Rule of 78s in credit transactions. The bill was referred to the House Committee on Financial Services on the same day. On April 10, 2001, the bill was referred to the Subcommittee on Financial Institutions and Consumer Credit, where it died with no further action taken.
A simple explanation would be as follows: Suppose the total finance charge for a 12 month loan was $78.00.
That figure is representative of the sum of digits by adding the numbers together..i.e. 12,11,10,9,8,7,6,5,4,3,2,1 = 78. If a person prepaid a consumer loan in 3 months, the financial institution would refund the sum of the "remaining" digits....(i.e. 9,8,7,6,5,4,3,2,1 or $45.00. They in essence would retain the first three (3) numbers...12,11,10 or $33.00. Thus the consumer would not receive as much of a refund if it were divided equally by 12 months ($6.50 per month). Under this scenario they would have received a refund of $58.50, much more beneficial than the $45.00 refund.
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.
For a 12 month loan, 12/78s of the finance charge
Finance charge
In United States law, a finance charge is any fee representing the cost of credit, or the cost of borrowing. It is interest accrued on, and fees charged for, some forms of credit. It includes not only interest but other charges as well, such as financial transaction fees...
is assessed as the first month’s portion of the finance charge, 11/78s of the finance charge is assessed as the second month’s portion of the finance charge and so on until the 12th month at which time 1/78s of the finance charge is assessed as that month’s portion of the finance charge. Following the same pattern, 24/300 of the finance charge is assessed as the first month’s portion of a 24 month precomputed loan.
Formula for calculating the unearned interest:
u = f * k(k+1)/n(n+1) u = unearned interest; f = total agreed finance charges; k = number of months paying off early; n = total term of loan in months
History
The earliest official use of the Rule of 78s to calculate the unearned portion of a loan’s finance charge was in IndianaIndiana
Indiana is a US state, admitted to the United States as the 19th on December 11, 1816. It is located in the Midwestern United States and Great Lakes Region. With 6,483,802 residents, the state is ranked 15th in population and 16th in population density. Indiana is ranked 38th in land area and is...
in 1935. Most loans in 1935 were for small amounts at low interest rates for short periods of time. It reduced the cost of loan calculations in a pre-computer era and was well suited for the small, short, and low interest rate loans of the era.
In the United States, the use of the Rule of 78s is prohibited in connection with mortgage refinancings and other consumer loans having a term exceeding 61 months.
On March 15, 2001, in the U.S. 107th Congress
107th United States Congress
The One Hundred Seventh United States Congress was a meeting of the legislative branch of the United States federal government, composed of the United States Senate and the United States House of Representatives. It met in Washington, D.C. from January 3, 2001 to January 3, 2003, during the final...
, U.S. Rep. John LaFalce
John J. LaFalce
John Joseph LaFalce is a former congressman from the state of New York; he served from 1975 to 2003.LaFalce was first elected to the 94th United States Congress in 1974 and re-elected to each succeeding Congress through the 107th, serving his Western New York congressional district for 28 years,...
(D-NY 29
New York's 29th congressional district
The Twenty-ninth district of New York is a congressional district for the United States House of Representatives which covers a portion of the Appalachian mountains in New York known as the "Southern Tier." It is represented by Tom Reed...
), introduced H.R. 1054, a bill to eliminate the use of the Rule of 78s in credit transactions. The bill was referred to the House Committee on Financial Services on the same day. On April 10, 2001, the bill was referred to the Subcommittee on Financial Institutions and Consumer Credit, where it died with no further action taken.
Precomputed Loan
The Rule of 78s deals with precomputed loans, loans whose finance charge is calculated before the loan is made. Finance charge, carrying charges, interest costs, or whatever the cost of the loan may be called, can be calculated with simple interest equations, add-on interest, an agreed upon fee, or any disclosed method. Once the finance charge has been identified, the Rule of 78s is used to calculate the amount of the finance charge to be rebated (forgiven) in the event that the loan is repaid early, prior to the agreed upon number of monthly payments. It should be understood that with precomputed loans, a borrower not only owes the lender the principal amount borrowed, but the borrower owes the finance charge as well. If $10,000 is lent and the precomputed finance charge is $3,000, the borrower owes the lender $13,000 at the time the loan is made, whereas a simple interest borrower owes the lender only the $10,000 principal and monthly interest on the unpaid principal.A simple explanation would be as follows: Suppose the total finance charge for a 12 month loan was $78.00.
That figure is representative of the sum of digits by adding the numbers together..i.e. 12,11,10,9,8,7,6,5,4,3,2,1 = 78. If a person prepaid a consumer loan in 3 months, the financial institution would refund the sum of the "remaining" digits....(i.e. 9,8,7,6,5,4,3,2,1 or $45.00. They in essence would retain the first three (3) numbers...12,11,10 or $33.00. Thus the consumer would not receive as much of a refund if it were divided equally by 12 months ($6.50 per month). Under this scenario they would have received a refund of $58.50, much more beneficial than the $45.00 refund.