## Interest calculation method

### Definition

The interest calculation method is defined by the quotient DAYS/DAY BASIS and, as a factor of the percentage calculation, results in the percentage calculation for the specific period, the interest calculation variant.

• Linear interest calculation:
Amount = calculation base * percentage rate / 100 * DAYS / DAY BASIS
• Exponential interest calculation:
Amount = Calculation base * (q ** (DAYS / DAY BASIS) - 1)
with the compounding factor q = 1 + percentage rate / 100 and
** as the power operator

The methods for calculating DAYS (number of days of corresponding calculation period) are:

1. 'act'
The actual number of days (calendar days) between the two dates are calculated.
2. '360'
The number of days between the dates M1/D1/Y1 and M2/D2/Y2 is calculated on the basis of
(Y2 - Y1) * 360 + (M2 - M1) * 30 + (D2 - D1).
The month is calculated using 30 days and the 31st of each month is ignored for interest calculatiion purposes.
Examples:
03/31 incl. to 04/02 incl. = 2 days
The 31st is not included.
12/01 incl. to 12/31 excl. = 30 days
The 31st is never included, so the addition of 'excl.' has no effect.
3. '360E'
The number of days between the dates M1/D1/Y1 and M2/D2/Y2 is calculated on the basis of
(Y2 - Y1) * 360 + (M2 - M1) * 30 + (D2 - D1).
The month is calculated using 30 days and the 31st of each month is considered to be the 30th, i.e. the 31st in D1 and D2 is reset to the 30th. This method is used on the Euromarkets.
Examples:
03/31 incl. to 04/02 incl. = 3 days
The 03/31 is treated as the 30th and included because of the addition
'incl.'.
12/01 incl. to 12/31 excl. = 29 days
12/31 is treated as the 30th, but not included because of the addition
'excl.'.

The following are defined as DAY BASIS:

1. 360

based on a year with 360 days.

2. 365

based on a year with 365 days.

3. 366

based on a year with 366 days.

4. 'actP'

The suffix 'P' stands for 'period' to reflect that the actual number of days in the period is used for the calculation. The days per year are calculated by multiplying the number of days in a period by the number of periods per year.

Example:
Interest calculation method: act/actP
Six-monthly interest payments: Frequency 6 months
Calculation period: 01/01/1999 - 07/01/1999
The resulting DAYS / DAY BASIS quotient is:
181 / 362 = 181 / ( 181 * ( 12 / 6 ) ).

5. 'actY'

The suffix 'Y' stands for 'year' to reflect that the actual number of days in the calendar year is used for the calculation - 366 days in a leap year, otherwise 365 days. If the calculation period extends across two calendar years, and one of these years is a leap year, the interest is calculated in two steps.

Example:
Interest calcualtion method: act/actY
Calculation period: 12/01/1999 - 01/09/2000
The resulting DAYS / DAY BASIS quotient is:
39 / 365,2046825 = 31 / 365 + 8 / 366.

The combinations of DAYS / DAY BASIS used in practice and supported in Treasury Management are:
act/360, act/365, act/366, 360/360, 360E/360, act/actP, act/actY