In memoriam F.G.

Nearly 60 years ago a friend of mine joked: "There are so many things you can expense from the amount you have to pay taxes for. What about expensing taxes, too?"

Well, if we intend to also apply the "new rule" to whatever we get as the interim tax amount, the actual application of the iteration will converge to a tax amount of 0.00. Applying algebra/calculus to the case would also return 0 as the only fixpoint if properly applied.

However, we may restrict the process to one step and then ask for an "effective tax amount" and an "effective rate" by which the original rate must be replaced to get the effective tax amount in one step, but now omitting the "right to expense taxes from tax base".

This way we get a perfectly well defined exercise in algebra without any iteration. Starting with the well-known formula for the tax amount

t, namely

- Code: Select all Expand viewCollapse view
`t = A*r`

where

A is the original base amount and

r the original tax rate, we get for the effective tax

T by expensing:

- Code: Select all Expand viewCollapse view
`T=(A-t)*r`

with the one-step-expense-rule and thus

- Code: Select all Expand viewCollapse view
`R = r - r*r`

for the effective rate. Applied to an original tax rate of (e.g.) 30% this results in 21%. Enjoy your meal.

The fiscal authority will, of course insist on sufficient influx. Their question must be: "If the one-step-expense is introduced by law, what nominal tax rate is then needed to get in the unchanged tax amount?" I'm afraid they won't find a solution in every case depending on the original rate. Have a lot of fun considering the political implications.

In the explained way RusselB may get a result for his question depending on whatver he exactly meant - and what I probably did not exactly understand.

On Windows 10: LibreOffice 7.0 and older versions, PortableOpenOffice 4.1.7 and older, StarOffice 5.2

---

Lupp from München