Calculate the Net Price Equivalent Rate in Decimals, Single Equivalent Rate in decimals, Amount of Trade Discount and Net Price based on the information given below. (Round your answer to 2 decimal places.) Item List Price Chain Discount Net Price Equivalent Rate (A) Single Equivalent Discount Rate (B) Amount of Trade Discount (C) Net Price (D) Ring $ 500 15/20
The Correct Answer and Explanation is:
To calculate the Net Price Equivalent Rate (A), Single Equivalent Discount Rate (B), Amount of Trade Discount (C), and Net Price (D) based on the given list price and chain discounts, we will follow a step-by-step method. Here’s the information provided:
- List Price: $500
- Chain Discount: 15/20
Step 1: Calculate the Net Price Equivalent Rate (A)
The chain discount 15/20 means that two discounts are applied sequentially:
First 15% then 20%.
To find the Net Price Equivalent Rate, we multiply the complements of each discount rate:Net Price Equivalent Rate=(1−0.15)×(1−0.20)=0.85×0.80=0.68\text{Net Price Equivalent Rate} = (1 – 0.15) \times (1 – 0.20) = 0.85 \times 0.80 = 0.68Net Price Equivalent Rate=(1−0.15)×(1−0.20)=0.85×0.80=0.68
So,
A. Net Price Equivalent Rate = 0.68
Step 2: Calculate the Single Equivalent Discount Rate (B)
The single equivalent discount rate is simply:Single Equivalent Rate=1−Net Price Equivalent Rate=1−0.68=0.32\text{Single Equivalent Rate} = 1 – \text{Net Price Equivalent Rate} = 1 – 0.68 = 0.32Single Equivalent Rate=1−Net Price Equivalent Rate=1−0.68=0.32
So,
B. Single Equivalent Discount Rate = 0.32
Step 3: Calculate the Amount of Trade Discount (C)
Amount of Trade Discount=List Price×Single Equivalent Rate=500×0.32=160.00\text{Amount of Trade Discount} = \text{List Price} \times \text{Single Equivalent Rate} = 500 \times 0.32 = 160.00Amount of Trade Discount=List Price×Single Equivalent Rate=500×0.32=160.00
So,
C. Amount of Trade Discount = $160.00
Step 4: Calculate the Net Price (D)
Net Price=List Price−Trade Discount=500−160=340.00\text{Net Price} = \text{List Price} – \text{Trade Discount} = 500 – 160 = 340.00Net Price=List Price−Trade Discount=500−160=340.00
So,
D. Net Price = $340.00
Summary
| Description | Value |
|---|---|
| Net Price Equivalent Rate (A) | 0.68 |
| Single Equivalent Discount Rate (B) | 0.32 |
| Amount of Trade Discount (C) | $160.00 |
| Net Price (D) | $340.00 |
Explanation
Trade discounts are reductions from the list price of an item offered by the seller to the buyer, often used in wholesale or bulk transactions. When multiple trade discounts are applied one after another, it is called a chain discount. In this case, the item has a list price of $500 and is subject to a chain discount of 15 percent and then 20 percent.
To understand how much the customer will actually pay, we start by finding the Net Price Equivalent Rate. This is done by subtracting each discount from 1 and then multiplying the remaining values. Subtracting 15 percent from 1 gives 0.85. Subtracting 20 percent from 1 gives 0.80. Multiply these together to get 0.68, which means the customer will pay 68 percent of the original list price. This rate is expressed as a decimal.
Next, the Single Equivalent Discount Rate represents the total discount that would have the same effect as applying both discounts. This is simply the complement of the net rate: 1 minus 0.68, which is 0.32 or 32 percent.
We calculate the Amount of Trade Discount by multiplying the list price of $500 by the single equivalent discount rate. This gives a discount of $160.
Finally, the Net Price is what the customer pays after the discount. Subtracting the trade discount from the list price results in a net price of $340.
Understanding these calculations helps businesses and buyers make informed financial decisions when dealing with complex discount structures.
