Successive Discounts

Retailers often mark down products in order to attract customers. We all like a good sale at our favorite store. This week we will discuss successive discounts.

Here is an example of a successive discount. I went to my favorite store and I found a purse on sale for 30% off. Luckily that day, the store also offered an additional 25% off the already discounted price. The original price of the purse was $120. How much did I pay for the purse if the sales tax rate is 8.25%?

Here is how I can find the final price:

Find the complements of the discounts:

• The complement of 30% is (100% – 30%) = 70% = 0.70.
• The complement of 25% is (100% – 25%) = 75% = 0.75.

Multiply the original price by the complements of the discounts:

• ($120)(0.70)(.75) = $63 This is the sale price.

Now find the total price including tax. To do this multiply the sale price by (1 + the sales tax)

• ($63)(1 + .0825) = $68.20 This is the total price I paid.

Find an example of a successive discount, either form your favorite store, in a weekly circular, or on the internet. Show all your calculations for finding the sale price (using the example above as a guideline) including the sales tax using the sales tax rate in your community. Discuss how most people miscalculate successive discounts in comparison to the calculation you posted and explain the reasons for the miscalculation most people do.