A supplier offers a series discount of 8/23. Find the net cost equivalent and the single discount equivalent. The net cost equivalent is (Round to four decimal places as needed.)
Answer (2)
The net cost equivalent after applying the series discounts of 8% and 23% is 0.7084, meaning the final price is 70.84% of the original. The single discount equivalent for these two discounts together is 0.2916, indicating a total discount of 29.16%.
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Calculate the complement of each discount rate: 1 − 0.08 = 0.92 and 1 − 0.23 = 0.77 .
Multiply the complements to find the net cost equivalent: 0.92 × 0.77 = 0.7084 .
Subtract the net cost equivalent from 1 to find the single discount equivalent: 1 − 0.7084 = 0.2916 .
The net cost equivalent is 0.7084 , and the single discount equivalent is 0.2916 , so the net cost equivalent is 0.7084 .
Explanation
Understanding the Problem We are given a series discount of 8/23, which means there are two discounts: 8% and 23%. We need to find the net cost equivalent and the single discount equivalent.
Calculating Net Cost Equivalent The net cost equivalent is the price after all discounts are applied, expressed as a decimal. To find it, we multiply the complements of each discount rate. The complement of a discount rate is 1 minus the discount rate.
Finding Complements of Discount Rates The discount rates are 8% and 23%, which can be written as 0.08 and 0.23, respectively. The complements of these rates are:
1 - 0.08 = 0.92 1 - 0.23 = 0.77
Calculating Net Cost Equivalent Now, we multiply these complements to find the net cost equivalent:
Net Cost Equivalent = 0.92 * 0.77 = 0.7084
Calculating Single Discount Equivalent The single discount equivalent is the single discount rate that would give the same final price as the series discount. We can find it using the formula:
Single Discount Equivalent = 1 - Net Cost Equivalent
Finding Single Discount Equivalent Using the net cost equivalent we calculated earlier (0.7084), we can find the single discount equivalent:
Single Discount Equivalent = 1 - 0.7084 = 0.2916
Final Answer Therefore, the net cost equivalent is 0.7084 and the single discount equivalent is 0.2916.
Examples
Imagine a store offers a series discount on a product. First, they offer a 10% discount for a loyalty card, and then an additional 20% discount for a special promotion. Understanding how to calculate the net cost equivalent helps customers determine the final price they will pay after all discounts are applied. This calculation is also useful for businesses to understand the actual revenue they will receive after applying multiple discounts. For example, if a product originally costs $100, with a 10% and 20% discount, the net cost equivalent is (1-0.10)*(1-0.20) = 0.9 * 0.8 = 0.72. Therefore, the final price is $100 * 0.72 = $72.
