To most consumers, simple mental arithmetic translates this into \(20% + 10% = 30%\) off. But computationally and financially, compound (or stacked) discounts do not work linearly. Each consecutive percentage reduction applies sequentially to the remainder of the previous price, not the original starting tag price.

When building a utility suite for xplosole, I needed to design a flexible calculation engine that could handle single markdowns, reverse percentages, and arbitrary multi-tier stacked discounts cleanly in the browser.

The Core Math: Sequential Reduction

When dealing with a single discount:

$$\text{Final Price} = \text{Original Price} \times \left(1 - \frac{\text{Discount}}{100}\right)$$

However, when stacking multiple discount tiers \(D = [d_1, d_2, \dots, d_n]\), each percentage compounds sequentially:

$$\text{Final Price} = \text{Original Price} \times \prod_{i=1}^{n} \left(1 - \frac{d_i}{100}\right)$$

For example, on a $100 item with $20%$ and $10%$ stacked discounts:

1. First Pass: \(100 \times (1 - 0.20) = \)80.00$

2. Second Pass: \(80 \times (1 - 0.10) = \)72.00$

Total Savings: $$28.00\ (28%)$, not $$30.00\ (30%)$.