# How to Compound Percentages

When determining a percentage of a percentage of a whole, for example 15% of 20% of 1,500, there is a common mistake that people make. **You do not want to add together 15% and 20% to get 35% and subtract that from 1,500.** This will result in the incorrect answer; the 15% must come from the 20%, not the whole. The correct way to solve this problem is to first convert the percentage into a fraction (0.2 in this case). Then take the whole (1,500) and subtract the decimal multiplied by the whole: 1500 – 0.2*1,500 = 1,200. Repeat the process to find 15% of 1,200 (1,020).

## Finding a Compound Percentage

This problem here highlights a common mistake that many people make. A TV’s regular price is $1,500, and the store is having a 20%-off sale. Store employees get 15% off the sale price.

**How much would an employee have to pay for this TV?** Now, the mistake that many people make is they see 20% and 15% and they add those together to get 35 percent.

Then they take 35% off of 1,500. The problem with this is that they’re taking the 15% off of the regular price, not off of the sale price.

What you have to do is take 20% off the regular price to get the sale price, and then take 15% off the sale price. To do this, we’re going to find the sale price by taking sale price equals 1,500 minus 20% times 1,500.

Now, we can rewrite this with a decimal as sale price equals 1,500 minus 0.2 times 1,500. To subtract this, we can take the sale price equals 1,500 minus 0.2 times 1,500 is 300.

1,500 minus 300 is 1,200. Our sale price is $1,200. To get to the employees’ price, we have to now take 15% off of the sale price. The employee price is 1,200 minus 15% times 1,200.

We’ll rewrite this as a decimal. We can say that the employee price is 1,200 minus 0.15 times 1,200. This number here, 0.15 times 1,200 is equal to 180.

We can say that the employee price is 1,200 minus 180. If you subtract 180 from 1,200, you find that the employee price is 1,020. For this TV an employee would pay $1,020.