Average percentage formula

Question

I have something like:

Price Quantity Tax (%)
  2.2    34     8
  1.3    29     7

And so on...

After that I get something like:

Subtotal: 112.6 (Sumation: Price x Quantity)
Discount: 23 (This is a percentage, it changes)
Tax (percentage): ?

What's the proper formula to calculate the "Average Tax" if I apply a variable discount?

Answer 1

let:

$S = subtotal$

$D = $discount percentage

$T = $tax percentage

$F =$ total after adjustment

$$F = (S - S*D)*(1.0+T)$$

$$F = S*(1.0 - D)*(1.0+T)$$

You are taking off a percentage first for the discount so that's where the $1-D$ comes from.

When you pay 8% tax on something your subtotal is actually multiplied by 1.08.

The "Average Tax" would be the total tax paid over many purchases divided by the total subtotal.