Interest numbers
Interest numbers (also interest numbers , discount numbers ) are used in the calculation of interest debits and credits in retail and banks when it is a matter of calculating the interest of various items according to days and according to the same interest rate . Interest numbers are always whole numbers, i.e. without decimal places. They are rounded commercially.
calculation
According to the known interest formulas , all daily interest rates are to be calculated individually for loans or the like with the same annual interest rate but different terms.
With the introduction of the commercial interest formula with interest divider and interest figures, this calculation can be simplified by converting the general daily interest formula:
The following applies:
- Z = interest amount
- K = principal amount
- p = interest rate in% (based on the divisor 100)
- t = number of days (as part of the year based on the divisor 360)
Note: With the commercial interest formula, according to the German interest calculation method, every month is calculated with a flat rate of 30 days, the year with 360 days. In other countries or for non-German currencies, other interest calculation methods are sometimes used. If the interest is to be calculated for a complete year, t and the divider 360 can be dispensed with, since they would be canceled out.
The dividend in the last formula that contains the variable figures for capital and day, ie interest rate or discount number , by shortening resulting in the number 360 with the fixed rate divisor is interest divider or in the jargon Zinsdivisor or Permanent .
This means that the conventional interest rate formula can be converted into the commercial interest rate formula as follows:
With
and
The following applies to the total interest for several capitals with the same interest rate but different terms:
Interest figures are always used in whole numbers (rounding up or down).
example
The following transactions took place in a current account in the 4th quarter of a year:
| Business transaction | Value date (value date) |
sales | balance |
|---|---|---|---|
| Balance carried forward | 30.09. | - | + 10,000.00 EUR |
| Incoming transfer | 16.10. | + 3,600.00 EUR | + 13,600.00 EUR |
| Transfer order | 11/14 | - EUR 2,200.00 | + 11,400.00 EUR |
The account is to be closed by December 31st and the interest credit is calculated at a credit interest rate of 0.5% pa.
For this purpose, the sales are recorded chronologically (according to their value date ) in an interest scale . With a current account, interest is paid on the balances until the next change (1 bank month = 30 days).
Here is a simplified example (the banks automatically calculate each value date individually even without account turnover; due to the necessary rounding of the daily interest figures, this can lead to slight deviations in practice):
| Value date | S / H | balance | Days | Interest rate |
|---|---|---|---|---|
| 30.09. | H | 10,000.00 EUR | 16 | 1600 |
| 16.10. | H | 13,600.00 EUR | 28 | 3808 |
| 11/14 | H | 11,400.00 EUR | 46 | 5244 |
| December 31 | H | 11,400.00 EUR | ||
| Sum of the credit interest figures: | 10,652 | |||
The sum of the credit interest figures (10,652) must now be divided by the interest divider. The result is the amount of credit interest for the quarter .
If the balance in the quarter was both debit and credit, or the interest rate has changed in the meantime, several calculations have to be made, since the interest divider has then changed.
See also
literature
- Thorsten Vehslage: Interest calculation methods - correct conversion of annual interest for daily periods , monthly for German law (MDR) 2001, issue 12, p. 673/674.