The Math of Stacking Discounts: Why 50% + 20% Is Not 70%

Have you ever seen a store advertise “Take an extra 20% off already reduced 50% clearance items” and thought you were getting 70% off?

While it sounds great, successive percentage discounts do not simply add together. Here is why the math works differently.

Consecutive Discounts Explained

When discounts are stacked, the second discount applies only to the remainder, not the original price.

Let’s look at a $100 jacket:

1. First discount (50% off):

   • $100 × 50% = $50 off.
   • Price after initial markdown = $50.00.

2. Second discount (Extra 20% off):

   • The 20% applies to the remaining $50, not the original $100!
   • $50 × 20% = $10 off.
   • Final price = $40.00.

3. Total Savings:

   • You saved $60 total ($50 + $10).
   • Your actual effective discount is 60%, not 70%.

Effective Discount Comparison Table

Primary Discount	Secondary Extra %	Effective Total Savings
20%	10%	28% (not 30%)
30%	20%	44% (not 50%)
40%	25%	55% (not 65%)
50%	20%	60% (not 70%)
50%	50%	75% (not 100%)

Always compute each discount sequentially to get the exact cost of your purchase!