Hi Bruce,
Suppose B is the cost before the tax, A is the cost after the tax is added and r is the tax rate. In your first example r = 10% = 10/100 = 0.1 and thus the tax is 0.1 × B and hence
A = B + 0.1 × B = (1 + 0.1) B
or
A = 1.1 B
which you stated. If you divide both sides of this equation by 1.1 you get
B = A/1.1
which is your second statement.
To retrace these steps for a general tax rate r the tax is r × B and hence
A = B + r × B
or
A = (1 + r) B
and thus
B = A/(1 + r).
Hence if r = 12% = 0.12 then
A = (1 + 0.12) B = 1.12 B
and
B = A/1.12
I hope this helps,
Penny
Bruce wrote back
Hi Penny, you replied to my question with this formula(i have changed the numbers):
Suppose B is the cost before the tax ($15), A is the cost after the tax is added and R is the tax rate (25%). In your first example R = 25% = 25/100 = 0.25 and thus the tax is 0.25× B=3.75 and hence
A = B + 0.25 × B =$228.75 ???? but then you say: (1 + 0.25)x B....where are you getting the "1" from based on the above?? so this should be:
A=(1+0.25)*15=$18.75 correct???. but how do you get the "1"if based on your comments R=0.25*$15=3.75?? then the formula should be:
A=(3.75+0.25)*15 = $60.....that i don't think is correct.
Can you please clarify.
Thanks Bruce.
Bruce,
I took out the common factor B.
B + 0.25 × B = 1 × B + 0.25 × B = (1 + 0.25) × B = 1.25 × B
so when B = $15 this is
1.25 × B = 1.25 × $15 = $18.75
Penny
