Net price equivalent rate (in decimals) Single equivalent discount rate (in decimals) 0.8302 0.1698 Chain discount Item LG Blu-Ray player List price Trade discount Net price 198 8/6/4
The Correct Answer and Explanation is:
To solve the given problem, we need to calculate the net price of the LG Blu-Ray player after applying a chain discount of 8/6/4 to the list price of $198, and also determine the net price equivalent rate and the single equivalent discount rate in decimal form.
Step 1: Understand the Discounts
A chain discount of 8/6/4 means three successive discounts are applied to the list price:
- First discount: 8%
- Second discount: 6%
- Third discount: 4%
Step 2: Convert Discounts to Multipliers
To find the net price, convert each percentage discount to a decimal multiplier:
- First multiplier: 1 − 0.08 = 0.92
- Second multiplier: 1 − 0.06 = 0.94
- Third multiplier: 1 − 0.04 = 0.96
Step 3: Multiply the Discounts
Multiply the three multipliers to get the net price equivalent rate:0.92×0.94×0.96=0.83020.92 \times 0.94 \times 0.96 = 0.83020.92×0.94×0.96=0.8302
This value is the net price equivalent rate in decimal form. It represents the fraction of the list price the buyer will actually pay after all discounts.
Step 4: Find the Net Price
Multiply the net price equivalent rate by the list price:198×0.8302=164.38198 \times 0.8302 = 164.38198×0.8302=164.38
So the net price is $164.38.
Step 5: Find the Single Equivalent Discount Rate
This is simply:1−Net Price Equivalent Rate=1−0.8302=0.16981 − \text{Net Price Equivalent Rate} = 1 − 0.8302 = 0.16981−Net Price Equivalent Rate=1−0.8302=0.1698
So the single equivalent discount rate in decimals is 0.1698.
Final Answers
- Net price equivalent rate (decimal): 0.8302
- Single equivalent discount rate (decimal): 0.1698
- Net price: $164.38
Explanation (300 Words)
A chain discount is a series of percentage discounts applied one after the other to a product’s list price. It is commonly used in wholesale and retail pricing. In this case, the LG Blu-Ray player has a list price of $198 and a chain discount of 8%, 6%, and 4%.
To find the total impact of these successive discounts, we must apply each one as a percentage off of the remaining price after the previous discount. This is different from simply adding the discount percentages together, because each discount is calculated on a different reduced base.
The easiest way to handle this is to convert each percentage into a decimal multiplier. For example, an 8% discount becomes 0.92, meaning the buyer pays 92% of the price after that discount. We repeat this process for the 6% and 4% discounts, using 0.94 and 0.96 respectively.
By multiplying all three decimal multipliers together, we get the net price equivalent rate—this tells us what portion of the original price the buyer pays after all discounts. Multiplying this rate by the list price gives us the final net price the buyer pays.
The single equivalent discount rate is the total reduction from the original price. It is calculated by subtracting the net price equivalent rate from 1. This gives a clear understanding of how much total discount the customer receives, expressed as a single percentage.
This method is useful for simplifying complex discount chains and is widely used in business and accounting to evaluate final prices and profitability.
