# Proving the Final Net Price with the Complement Method

## Introduction

The complement method can also be used with chain discounts as follows:
1. First subtract each discount from 100 percent to find its complement.
2. Then the complements is multiplied to find the percent, which represent the net price rate to be paid.
3. The complement method can also be used to find the dollar amount of the discount.
4. The single equivalent discount (SED), or the complement of the net-price rate is multiplied by the list price to find the discount.
SED = Complement of Net-Price Rate
Discount = List Price × SED

### Example: Find the final net price.

Zoho Appliances has a super freezer in stock it wants to clear out. The super freezers originally sold for \$1,185. Zoho Appliances is offering a discount of 25 percent less 15 percent, also written as 25/15. What is the final net price of the super freezer?
1. Find the complements. Complement of 25% is 75%. Complement of 15% is 85%.
2. Find the net-price rate. Net Price Rate = Product of Complements of (Chain-Discount Rates) = 75% × 85% = 63.75%
3. ind the net price. Net Price = List Price × Net-Price Rate = \$1,185 × 63.75% = \$755.44

### Practice: Find the net-price rate, the net price, the SED, and the discount.

Final Net Price
List Price Chain Discounts Net-Price Rate Net PriceSED Discount
\$950.00 25%/10% ??? ?????? ???
\$1375.00 30%/20% ??? ?????? ???
\$1975.00 20%/15% ??? ?????? ???