Tutoring high school math, you see financial word problems. The tutor gives an example.
Problem: At 12% tax, what discount will lead to paying exactly the sticker price after tax?
The final price, f, is as follows:
f = (1-discount)(1+tax)p
Where p is original price, and discount and tax are in decimals, not percent (eg, tax is 0.12 rather than 12%)
We need f=p, at tax=0.12:
Dividing both sides by p we get
Then, dividing by 1.12,
0.8929 = 1-discount
Rearranging we get
discount = 1-0.8929 = 0.1071 or 10.71%.
Apparently, at 12% tax, a discount of 10.71% is needed to equate the after-tax price to the sticker price.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.