interesting math issue

[Guest]

Hi all,

So here is a little brain teaser that I need to solve.

I need to calculate a tax amount based on a certain $ amount. However the
caveat is that the tax amount is a component of the $ amount. So, in my
example:-

Amount: $10,000
Formula for Tax Amount: Amount*0.0035

Howerver, Tax Amount needs to be included in Amount.

Can this be solved?

[Michael C]

Re: interesting math issue

<param@communit y.nospamwrote in message
news:%23RY8FCAc HHA.208@TK2MSFT NGP05.phx.gbl.. .

Hi all,
>
So here is a little brain teaser that I need to solve.
>
I need to calculate a tax amount based on a certain $ amount. However the
caveat is that the tax amount is a component of the $ amount. So, in my
example:-
>
Amount: $10,000
Formula for Tax Amount: Amount*0.0035
>
Howerver, Tax Amount needs to be included in Amount.
>
Can this be solved?

So Amount = OrigAmount * (1 + 0.0035) ?

OrigAmount = Amount / (1.0035)
OrigAmount = $9965.12

That's assuming I understand your question.

Michael

[C-Services Holland b.v.]

Re: interesting math issue

param@community .nospam schreef:

Hi all,
>
So here is a little brain teaser that I need to solve.
>
I need to calculate a tax amount based on a certain $ amount. However the
caveat is that the tax amount is a component of the $ amount. So, in my
example:-
>
Amount: $10,000
Formula for Tax Amount: Amount*0.0035
>
Howerver, Tax Amount needs to be included in Amount.
>
Can this be solved?
>
>

Basic math:
OrgAmount=Taxed amount/1.0035


--
Rinze van Huizen
C-Services Holland b.v

[Guest]

Re: interesting math issue

So I guess to understand correctly, let us assume the following 3 variables:

FinalAmount: $10,000
Tax Amount: = 10,000*0.0035 = $35

But the tricky part the final amount always needs to be 10,000. So if we
back the amount down to (10000-35) = 9965, then that will now change the tax
amount.


"Michael C" <nospam@nospam. comwrote in message
news:%23rNIwKAc HHA.260@TK2MSFT NGP02.phx.gbl.. .

<param@communit y.nospamwrote in message
news:%23RY8FCAc HHA.208@TK2MSFT NGP05.phx.gbl.. .

>Hi all,
>>
>So here is a little brain teaser that I need to solve.
>>
>I need to calculate a tax amount based on a certain $ amount. However the
>caveat is that the tax amount is a component of the $ amount. So, in my
>example:-
>>
>Amount: $10,000
>Formula for Tax Amount: Amount*0.0035
>>
>Howerver, Tax Amount needs to be included in Amount.
>>
>Can this be solved?

>
So Amount = OrigAmount * (1 + 0.0035) ?
>
OrigAmount = Amount / (1.0035)
OrigAmount = $9965.12
>
That's assuming I understand your question.
>
Michael
>

[Andrew Morton]

Re: interesting math issue

param@community .nospam wrote:

So I guess to understand correctly, let us assume the following 3
variables:
FinalAmount: $10,000
Tax Amount: = 10,000*0.0035 = $35
>
But the tricky part the final amount always needs to be 10,000. So if
we back the amount down to (10000-35) = 9965, then that will now
change the tax amount.

No,
final amount=initial amount+tax amount (eqn 1)

where
tax amount=initial amount*tax rate (eqn 2)

substituting (eqn 2) into (eqn 1) gives
final amount=initial amount+(initial amount*tax rate)

which is
final amount=initial amount*(1+tax rate) (eqn 3)

divide both sides of (eqn 3) by (1+tax amount) and re-arrange to give
initial amount=final amount/(1+tax amount)

Putting in the figures final amount=10,000 and tax rate=0.0035:
initial amount=10,000/(1+0.0035)
initial amount=9965.12

HTH

Andrew

[C-Services Holland b.v.]

Re: interesting math issue

param@community .nospam schreef:

So I guess to understand correctly, let us assume the following 3 variables:
>
FinalAmount: $10,000
Tax Amount: = 10,000*0.0035 = $35
>
But the tricky part the final amount always needs to be 10,000. So if we
back the amount down to (10000-35) = 9965, then that will now change the tax
amount.
>

That is not correct. The final amount is 10000 which includes the 0.35
percent tax. You're making the mistake of calculating the tax over an
amount that already has the tax included. So to get the untaxed amount
you divide by 1.0035

10000/1.0035 = 9965.12 (approx)
So the taxamount = 34.88 (approx)

I say approx because there's some rounding in there.

The formula is a=b*(1+c)
therefore b = a/(1+c)
where
a=totaltaxedamo unt
b=untaxedamount
c=taxpercentage
--
Rinze van Huizen
C-Services Holland b.v