Reversing a Discount Percentage

May 11, 2016 at 12:05 pm

Removing a discount is not as simple as adding the discounted amount back in if the logic for applying the discount applies it on the new number. If a post-discount operation can be performed then the math is much easier (add x * discount to the discounted price.

A discount applied to the original number is slightly tricker. For the math below, discount is a percentage and cost will be a dollar figure.

discount = 10%
cost = $100

A discounted cost can be calculated discount to cost:

discounted_cost = cost - (cost * discount) => $90

Simply applying an addition of discount does not work, it results in a new cost that’s slightly less than the expected (original) cost:

new_cost = cost + (cost * discount) => $110
discounted_cost = new_cost - (new_cost * discount) => $99

A formula with one unknown increase used to balance discount against the original cost can be written as:

(cost + cost * increase) - ((cost + cost * increase) * discount) = cost

Simplifying that formula:

(x + (x * z)) - ((x + x * z) * y) = x
z => y/(-y + 1)

Now a formula increase given discount can be written:

increase = discount / (-discount + 1) => 0.1111

And a formula for new_cost given only discount:

new_cost = cost + cost * (discount / (-discount + 1)) => $111.1111

Calculating the new total and proving it balances with the original cost:

new_total = new_cost - (new_cost * discount) => $100

A simple function for Python could be written as follows:

def remove_discount(cost, discount):
    return cost + cost * (discount / (-1 * discount + 1))

§

May 2016

Can’t find what you’re looking for? Try hitting the home page or viewing all archives.