## Need a method of getting a number that's circular

### Need a method of getting a number that's circular

The subject line is, imo, somewhat misleading as the amount calculated has to be included in the total that the amount is calculated from.

Rate is 30% of Gross, but Rate is added to Gross, giving a new Rate.

What I'm looking for is something like 30%*(G+30%*G)=30%*G
Both G and 30%*G are to be rounded to 2 decimal places

G has to be between 989 and 1787
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RusselB
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### Re: Need a method of getting a number that's circular

percentage calculations...

30%*(G+30%*G)=30%*G
The root of this equotion is the 0 - and only the zero: G must be 0 !

A sample with a simple, and other small numbers:

8 * 25% = 2
8 + 2 = 10

2 / 10 * 100 = 20%
The result is 20% but not not 25% !!!

In other words - If G represents same number in the equotion:
30%*(G+30%*G)=30%*G

then you can simplify it with the G:
30%*(1+30%*1)=30%*1

Change the % to decimal fraction
0.3*(1+0.3)=0.3

0.3*(1.3)=0.3

Result:
0.39 <> 0.3 !!!

Or - maybe - I not understood, what you want to achieve...
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Zizi64
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### Re: Need a method of getting a number that's circular

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.
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Lupp from München

Lupp
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### Re: Need a method of getting a number that's circular

Ok. Allow me to clarify.
I'm moving into a RGI (rent geared to income) building.
One of my income sources has a base monthly amount of \$989
They will also cover the rent up to \$798.
The RGI rate is 30% of the gross income.
Since the calculated rent, up to the \$798 gets added to the \$989, the RGI also increases a bit due to the increased gross income.

Hopefully this further explanation will help.
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RusselB
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### Re: Need a method of getting a number that's circular

To clarify: "They will also cover the rent up to \$798."

Is the 798 the total amount of Rent, or the income on which rent is calculated?
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RoryOF
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### Re: Need a method of getting a number that's circular

There should be a contract o any kind of legal text defining the rules of calculating whatever needs be calculated here. Can you quote the respective part of it?
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Lupp from München

Lupp
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### Re: Need a method of getting a number that's circular

@RoryOF: The \$798 is the maximum amount for the rent that will be covered by this employer.

@Lupp: There probably is specific text, but I don't have access to it right now.
The general terms for calculating the RGI is that the rent will be 30% of the previous month's gross earnings.
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RusselB
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