This calculation shows that theoretically, had the various transactions been under contemplation on December 31, the focal date, payment of the total $2,650 could equitably have been made with a discount of $80.28. The interest (or discount) on $2,650 for 1 day is 44⅙ cents. A discount amounting to $80.28 can therefore be demanded on $2,650 only as the result of an offer to prepay 182 days (80.28 ÷ .44⅙ = 182) before the payments are equitably due. Hence, payment of $2,650 without discount would settle the account equitably 182 days after the focal date, or on July 1. That this is true can easily be proved by using July 1 as the settlement date and figuring as for a current account. It will be found that interest on the overdue items on that date amounts to $10.42, while the discount on the item not yet due amounts to $10.33; the difference .09 not being a large enough fraction (9 ÷ 44⅙) to justify payment one full day earlier.
The 100% Method.—A short method of calculation may be used, employing the 100% per day method. Any date may be taken as a focal date, and very frequently the date of the first or last transaction is used. In the illustration below, November 30 of the previous year is taken as the focal date so that the expired time on each item is immediately indicated by the number of the month and the day in the “date of value” column. The use of the 100% per day method makes the calculation of interest on each item a simple matter of multiplication by time and amount, i.e., it reduces each amount to a “day-dollars” figure, and on that basis one day’s interest on the account total is equal to that total, and therefore the divisor in the division made to determine the focal date is the amount of the account. This greatly simplifies all the operations. Sometimes the expired time is calculated by calendar months and days, converting fractions of a month on a 30-day basis. The method is used in the illustration below, where the problem shown above by the accurate interest method is solved by the 100% method.
The “month-dollars” column divided by the “amount” column gives 6, shown in the “equated date, months” column, with a remainder of 2,500. This is reduced, by multiplication by 30, to day-dollars and carried to that column, whose total, 80,100, is divided by 2,650, giving 30 as shown in the “equated date, days” column. The equated date is therefore June 30 (6/30). The one day’s difference between this and the other method is accounted for because each calendar month is counted as 30 days.
| Time | Equated Date | |||||||
|---|---|---|---|---|---|---|---|---|
| Months | Days | Amount | Month- Dollars | Day- Dollars | Months | Days | ||
| 2 | 4 | $ 100 | $ 200 | $ 400 | ||||
| 4 | 2 | 350 | 1,400 | 700 | ||||
| 4 | 10 | 200 | 800 | 2,000 | ||||
| 8 | 1 | 2,000 | 16,000 | 2,000 | ||||
| $2,650 | )$ 18,400 | $ 5,100 | 6 | 30 | ||||
| 15,900 | ||||||||
| $ 2,500 | ||||||||
| 30 | 75,000 | 6 | 30 | |||||
| $80,100 | ||||||||
| 79,500 | ||||||||
| $ 600 | ||||||||
Compound Equation.—Where the account has both debits and credits, the estimate is made similarly. Calculation of the month- and day-dollars is made for each side separately. At this point the totals on both sides are combined to find the balance of the account and the balance of the discounts, and these two balances are used to find the equated date. If the balance of the account is on the same side as the balance of the discount, the equated date is forward from the focal date because, if settlement were made on that date, the man who owes the balance is entitled to the theoretical discount also. If the balance of the account and the balance of interest are on different sides, the count is backward from the focal date. The following account and solution will illustrate:
| S. L. Davis | |||
| 19— | 19— | ||
| Mar. 8 Mdse. net | 1,000.00 | Apr. 30 Note, 30 da., 6% | 500.00 |
| June 20 ” n/30 | 1,500.00 | Aug. 30 Cash | 1,500.00 |
| Sept. 5 ” n/60 | 2,000.00 | Sept. 10 Note, 60 da., no interest | 2,000.00 |
| Debits: | ||||||||
|---|---|---|---|---|---|---|---|---|
| Expired Time | Interest | |||||||
| Months | Days | Amount | Month-Dollars | Day-Dollars | ||||
| 3 | 8 | $1,000 | $ 3,000 | $ 8,000 | ||||
| 7 | 20 | 1,500 | 10,500 | 30,000 | ||||
| 11 | 4 | 2,000 | 22,000 | 8,000 | ||||
| Totals | $4,500 | $35,500 | $46,000 | |||||
| Credits: | ||||||||
| 4 | 30 | $ 500 | $ 2,000 | $15,000 | ||||
| 8 | 30 | 1,500 | 12,000 | 45,000 | ||||
| 11 | 9 | 2,000 | 22,000 | 18,000 | ||||
| Totals | $4,000 | $36,000 | $78,000 | |||||
| Balances: | ||||||||
| Amount | Dr. $500 | |||||||
| Interest | Cr. $500 | Cr. $32,000 | ||||||
Dividing we get 1 month, 64 days, i.e., 3 months, 4 days. The balances being on opposite sides, the equated date is 3 months, 4 days, backward from November 30 (11/30), i.e., 11/30 - 3/4 = 8/26 or August 26. Equitable settlement could therefore be made by interest-bearing note for $500, dated August 26, or by cash payment of $500 plus interest on $500 from August 26 until date of actual settlement, as would be the case had the account been handled as an account current with adjustment as of August 26.
The Cash Balance.—When an account has been equated, to determine the cash sum which will be required for equitable settlement on a given date subsequent to the equated date, the balance of the account plus interest on that balance from the equated date to the date of settlement will be the correct amount. This amount is technically called the cash balance of the account. It is exactly the same as the adjusted balance of an account current, and may be determined by such adjustment of the account instead of by the method of equation of payments just described.
Interest on Partial Payments.—Under the heads of accounts current and equation of payments, the question of partial payments on open account has been treated. There remains to be discussed a statement of the practices governing partial payments on notes. Two methods of calculating are in use, the legal or United States method and the so-called merchants’ method. The merchants’ method is used for short-time notes and on any other kind by agreement. The method is exactly similar to that of adjustment of current accounts. Interest is charged on the face of the note from its date of issue till its due date, and allowed on each partial payment from its date of payment till the due date of the note. The difference between the sum of the face of the note plus its interest and the partial payments plus their interest accruals is, of course, the balance due.