# calculating percentage of percentage

1. ## calculating percentage of percentage

How does one get "X" in excel from the formula 100=X-(X*21%)-(X*2.7%) ?

Background: Credit cards take a percentage of the VAT inclusive amount. I would like this credit card cost to be automatically included in total VAT inclusive cost.

For example, VAT is 21% and credit card fee is 2.7% on the total VAT inclusive amount. A theoretical VAT inclusive amount of 121 would have a credit card cost of 3.267 and a VAT cost of 21, so the net amount is not 100 but 96.733

What would the VAT inclusive amount need to be to have a net amount of 100? And how does one put this in an excel formula?

2. ## Re: calculating percentage of percentage

100=X-(X*21%)-(X*2.7%)
Convert percentage to decimals:
100=X-(X*0.21)-(X*0.027)
Divide both side by X
100/X=X/X-(x/x*0.21)-(x/x*0.027)=1-0.21-0.027
Multiply both sides by x, then divide both sides by (1-0.21-0.027)
X=100/(1-0.21-0.027)

I think.

3. ## Re: calculating percentage of percentage

"Divide both side by X" (x<>0)

Regards

4. ## Re: calculating percentage of percentage

Ha

100=X-(X*21%)-(X*2.7%)
Convert percentage to decimals:
100=X-(X*0.21)-(X*0.027)
Factorise right side by X:
10=X*(1-0.21-0.027)
Divide both side by (1-0.21-0.027):
X=100/(1-0.21-0.027)

Better?

Much better!

6. ## Re: calculating percentage of percentage

Originally Posted by yudlugar
Ha

100=X-(X*21%)-(X*2.7%)
Convert percentage to decimals:
100=X-(X*0.21)-(X*0.027)
Factorise right side by X:
10=X*(1-0.21-0.027)
Divide both side by (1-0.21-0.027):
X=100/(1-0.21-0.027)

Better?
Sometimes life is so, so simple one doesn't see it and needs to be told. Thank you!!!

7. ## Re: calculating percentage of percentage

I'd argue that the other one is valid when x=0 also though, as it would give you 0/0 which is possible

8. ## Re: calculating percentage of percentage

Haha!

So you claim - mathematicians have been debating the true definition of 0/0 for centuries!

9. ## Re: calculating percentage of percentage

I like the:
0/0=y
therefore
0*y=0
therefore y can be any number
arguement...

10. ## Re: calculating percentage of percentage

Yes! A classic Christmas Cracker teaser for budding young mathematicians everywhere!

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