What is the (net price equivalent rate-in decimals, Single Equivalent discount rate-in decimals, trade discount and net price)of a digital camera with List price $450 and chain discount 8/3?
Net Price Equivalent Rate (in decimals): 0.8
Single Equivalent Discount Rate (in decimals): 0.2
Trade Discount: 8/3
Net Price: $360
To find the net price equivalent rate, single equivalent discount rate, trade discount, and net price of a digital camera with a list price of $450 and a chain discount of 8/3, follow these steps:
Step 1: Convert the chain discount to a decimal.
- The chain discount, 8/3, can be expressed as 2.67 (when rounded to decimal places).
Step 2: Calculate the net price equivalent rate (NPER).
- The NPER can be found by subtracting the chain discount from 1.
- NPER = 1 - 2.67 = -1.67
Step 3: Calculate the single equivalent discount rate (SED).
- The SED is the equivalent discount rate if all discounts were combined into one discount.
- SED can be found by dividing the NPER by the number of discounts (in this case, 1 discount).
- SED = -1.67 / 1 = -1.67
Step 4: Calculate the trade discount.
- Trade discount represents the total discount given.
- Trade discount = List price x NPER = $450 x -1.67 = -$750.50
Step 5: Calculate the net price.
- Net price is the final price after deducting the trade discount from the list price.
- Net price = List price + Trade discount = $450 + (-$750.50) = -$300.50
Thus, the values are:
- Net Price Equivalent Rate (NPER): -1.67 (or -167%)
- Single Equivalent Discount Rate (SED): -1.67 (or -167%)
- Trade Discount: -$750.50
- Net Price: -$300.50
To find the net price equivalent rate in decimals, we need to calculate the complement of the chain discount rate.
Step 1: Convert the chain discount format from a fraction to a decimal.
The chain discount rate is 8/3. To convert it to a decimal, divide the numerator (8) by the denominator (3):
Chain discount rate = 8 รท 3 = 2.67 (rounded to two decimal places)
Step 2: Calculate the complement of the chain discount rate.
Complement = 1 - Chain discount rate
Complement = 1 - 2.67 = -1.67 (rounded to two decimal places)
The net price equivalent rate in decimals is approximately -1.67.
Next, we can find the single equivalent discount rate (SED) in decimals.
Step 3: Determine the number of chain discounts.
The chain discount is 8/3, which means there are 3 discounts with a total discount of 8.
Step 4: Calculate the SED rate.
SED rate = Chain discount rate / (1 - (Number of discounts x Chain discount rate))
SED rate = 8/3 / (1 - (3 x 8/3))
SED rate = 8/3 / (1 - 8/3)
SED rate = 8/3 / (1 - 2.67/1)
SED rate = 8/3 / (1 - 2.67)
SED rate = 8/3 / -1.67
SED rate = -1.5 (rounded to one decimal place)
The single equivalent discount rate in decimals is approximately -1.5.
Finally, we can calculate the trade discount and the net price.
Step 5: Calculate the trade discount.
Trade discount = List price x SED rate
Trade discount = $450 x (-1.5)
Trade discount = -$675
The trade discount for the digital camera is -$675.
Step 6: Calculate the net price.
Net price = List price + Trade discount
Net price = $450 + (-$675)
Net price = -$225
The net price for the digital camera is -$225.