From TAEG to Commission

README.md

From TAEG to Commission

Understanding TAEG

TAEG is the Taux Annuel Effectif Global, it is the cost of money for a year with the current fees on the loan.

From an amortization table, you can compute it like that:

+------------+--------------+
| Date       +  Cash flow   |
+------------+--------------+
| 2024-01-01 | - 10 000.00  |
| 2024-02-01 | +  3 360.53  |
| 2024-03-01 | +  3 360.53  |
| 2024-04-01 | +  3 360.53  |
+------------+--------------+

>>> import numpy_financial as npf
>>> round(((1 + npf.irr([-10000, 3360.53, 3360.53, 3360.53])) ** 12 - 1) * 100, 2)
5.0

Difference between TAEG and TEG

The TAEG is the indicator used in France for loans contracted with people (B2C). It is the internal rate of return of the money.

The TEG is the indicator used in France for loans contracted with companies (B2B). It is interest rate of the money.

TAEG describe money that once collected is revinvested again (investment of money). TEG describe money that once collected is not reinvested again (cost of money).

  >>> import numpy_financial as npf
  >>> TAEG = round(((1 + npf.irr([-10000, 3360.53, 3360.53, 3360.53])) ** 12 - 1) * 100, 2)
  >>> TEG = round(npf.irr([-10000, 3360.53, 3360.53, 3360.53]) * 12 * 100, 2)
  >>> (10000, 10081.59, TAEG, TEG)
(10000, 10081.59, 5.0, 4.89)

How to compute the commission or fees for a given TAEG and a given period

The TAEG is based on the time in between repayment collection. In France we take that a year is 360 days and a month is 30 days.

If we want to be precise, we can compute the exact number of days between two recollection.

For monthly repayment the formula is much easier:

>>> from decimal import Decimal

>>> TAEG = Decimal(5.00) / 100
>>> installments_count = 3  # Number of months

>>> monthly_rate = (1 / (1 + TAEG)) ** Decimal(1/12)
>>> commission_percentage = ((1 - monthly_rate) / (monthly_rate - monthly_rate ** (installments_count + 1))) * installments_count - 1
>>> round(commission_percentage * 10_000, 2)
Decimal('81.59')

Normalized vs Extended

If you want to be more specific and rather than using the Normalized months convention use the real number of days in between two installments, you need to use this computation method:

>>> from dateutil.relativedelta import relativedelta
>>> from decimal import Decimal
>>> import datetime as dt

>>> TAEG = Decimal(5.00) / 100
>>> installments_count = 3  # Number of months
>>> payout_date = dt.date(2024, 1, 1)

>>> sk = Decimal(0)
>>> for i in range(1, installments_count + 1):
...     current_date = payout_date + relativedelta(months=i)
...     sk += 1 / ((1 + TAEG) ** (Decimal((current_date - payout_date).days) / 365))
...
>>> installments_count / sk - 1
Decimal('0.008136979965497172560519382')