Single Trade Discount and Discount Series || Business Math
Summary
TLDRThis script delves into the concept of trade discounts, explaining key terms like suggested retail price, trade discount, net price, and discount rate. It outlines formulas for calculating trade discount and net price, and illustrates these with examples involving various discount rates. The script further explores trade discount series, showcasing how multiple discounts are applied sequentially and how to calculate the single equivalent rate, concluding with the net price and trade discount for different scenarios.
Takeaways
- 📚 The script introduces the concept of trade discounts, explaining it as the amount of discount a wholesaler or retailer receives off the list price of an item.
- 🔢 It defines 'Net Price' as the price paid by a retailer after applying the trade discount to the list price.
- 📉 The 'Discount Rate' is the percentage of the list price that is given as a discount to the retailer.
- 📝 The formula for calculating the trade discount is presented as Trade Discount (TD) = Discount Rate (DR) * List Price (LP).
- ➖ The net price is calculated by subtracting the trade discount from the list price, symbolized as Net Price (NP) = LP - TD.
- 💡 An example is given to illustrate the calculation of trade discount and net price for an item listed at 10,000 pesos with a 20% discount rate.
- 🛒 The script discusses the concept of trade discount series, where multiple discounts are applied successively to the list price.
- 🔄 The reasons for using trade discount series include encouraging volume purchases, promoting special or seasonal items, and enticing new clients.
- 🧮 The formula for calculating the net price with a series of discounts is provided, involving multiple applications of 1 minus the discount rate.
- 📉 The single rate equivalent (SRE) of a series of discounts is calculated by multiplying the inverse of each individual discount rate.
- 📱 An example of a new cell phone model subject to multiple discounts is used to demonstrate the calculation of the single rate equivalent and net price.
Q & A
What is the definition of 'suggested retail price' or 'catalog price'?
-The suggested retail price or catalog price refers to the price at which a manufacturer suggests an item should be sold to customers.
What does 'trade discount' mean in the context of the transcript?
-Trade discount is the amount of discount that a wholesaler or retailer receives off the list price, which is the difference between the list price and the net price.
How is the 'trade discount' calculated according to the transcript?
-The trade discount is calculated as the product of the discount rate and the list price, represented as TD = DR * LP, where TD is the trade discount, DR is the discount rate, and LP is the list price.
What is the formula for determining the 'net price' as mentioned in the transcript?
-The net price is determined by subtracting the trade discount from the list price, which can be represented as NP = LP - TD, where NP is the net price, LP is the list price, and TD is the trade discount.
What is the significance of the 'discount rate' in trade discount calculations?
-The discount rate is the percentage rate applied to the list price to determine the trade discount, and it represents the amount to be paid by the retailer to the manufacturer.
Can you provide an example from the transcript where the net price is calculated after a 20% discount on a 10,000 peso item?
-Yes, in the example, a 10,000 peso item with a 20% discount results in a trade discount of 2,000 pesos (10,000 * 0.20), and the net price is 8,000 pesos (10,000 - 2,000).
How does the transcript explain the concept of 'trade discount series'?
-A trade discount series, as explained in the transcript, is when a manufacturer offers two or more trade discount percentages that apply to the same item price, encouraging volume purchases, promoting special or seasonal items, and enticing new clients.
What is the formula for calculating the 'net price' when there is a series of trade discounts?
-The formula for calculating the net price with a series of discounts is NP = LP * (1 - DR1) * (1 - DR2) * ... * (1 - DRn), where NP is the net price, LP is the list price, and DR1, DR2, ..., DRn are the discount rates.
How is the 'single trade discount equivalent' determined when there are multiple discount rates?
-The single trade discount equivalent is determined by the formula SRE = 1 - (1 - DR1) * (1 - DR2) * ... * (1 - DRn), where SRE is the single equivalent rate, and DR1, DR2, ..., DRn are the individual discount rates.
What is the significance of calculating the 'single trade discount equivalent'?
-Calculating the single trade discount equivalent helps to understand the overall discount rate that is equivalent to a series of discounts, which can simplify the comparison and understanding of the total discount being offered.
Outlines
📚 Introduction to Trade Discounts
The script begins with an introduction to trade discounts, explaining key terms such as suggested retail price, trade discount, net price, and discount rate. It defines trade discount as the amount of discount a wholesaler or retailer receives from the list price. The script then introduces formulas for calculating trade discount (td = dr * lp) and net price (np = lp - td), where 'td' is trade discount, 'dr' is discount rate, and 'lp' is list price. An example is provided to illustrate the calculation of trade discount and net price for an item listed at 10,000 pesos with a 20% discount rate.
🔢 Calculating Net Price and Trade Discount
This paragraph delves deeper into the calculation of net price and trade discount, using an example where a factory sells goods at a retail price with a given discount rate. The process involves converting the discount rate to a decimal, applying it to the retail price to find the net price, and then determining the trade discount by subtracting the net price from the list price. The example provided involves a 20,000 peso item with a 15% discount rate, resulting in a net price of 17,000 pesos and a trade discount of 3,000 pesos.
📉 Understanding Trade Discount Series
The script explains the concept of trade discount series, which involves applying multiple discount rates sequentially to the list price of an item. It outlines the reasons for using discount series, such as encouraging volume purchases, promoting special or seasonal items, and enticing new clients. The paragraph also provides a formula for calculating the net price in a series of discounts and the single equivalent rate of discount. An example is given where a refrigerator is sold with a list price of 25,000 pesos and trade discounts of 30%, 20%, and 10%, resulting in a net price of 12,600 pesos and a total trade discount of 12,400 pesos.
📱 Applying Trade Discount Series to a Cell Phone Example
This paragraph applies the concept of trade discount series to a new model of cell phone priced at 40,500 pesos with three different discount rates: 15%, 20%, and 5%. The script guides through the process of calculating the net price and the single equivalent discount rate for the series. The calculation shows that the single equivalent discount rate is 49.6%, and the net price after applying all discounts is 26,163 pesos. Additionally, the total trade discount for the cell phone is calculated to be 14,337 pesos.
📈 Summarizing Trade Discount Calculations
The final paragraph summarizes the formulas and processes discussed in the script for calculating net prices and trade discounts, both for single discounts and discount series. It reiterates the importance of understanding discount rates and their impact on the final price of goods. The summary serves as a recap of the key points and formulas introduced throughout the script, ensuring a clear understanding of trade discount calculations.
Mindmap
Keywords
💡Suggested Retail Price (SRP)
💡Trade Discount
💡Net Price
💡Discount Rate
💡List Price
💡Trade Discount Series
💡Single Equivalent Rate (SER)
💡Chain Discount
💡Volume Purchases
💡Seasonal Items
Highlights
Definition of terms related to trade discounts, including suggested retail price, catalog price, trade discount, net price, and discount rate.
Explanation of the trade discount formula: TD = DR * LP, where TD is trade discount, DR is discount rate, and LP is list price.
Derivation of the net price formula: NP = LP - TD, and its alternative expression NP = LP * (1 - DR).
Example calculation of trade discount and net price for an item listed at 10,000 pesos with a 20% discount rate.
Method to determine the trade discount and net price when the retail price and discount rate are known but not the net price.
Example involving a 20,000 pesos item with a 15% discount rate to find the amount paid by a store and the trade discount.
Process to find the discount rate when the net price and trade discount are known, using the formula DR = (TD / LP).
Explanation of trade discount series and their use in encouraging volume purchases, promoting special items, and enticing new clients.
Calculation of net price and trade discount for an item with a series of discounts (30%, 20%, and 10%).
Determination of the single trade discount rate equivalent to a series of discounts using the formula SRE = 1 - (product of (1 - DRi)).
Example of a new cell phone model with a list price of 40,500 pesos subject to a series of discounts and the calculation of the single rate equivalent.
Method to calculate the net price for an item given its list price and the single trade discount rate equivalent.
Calculation of the total trade discount for the cell phone example by subtracting the net price from the list price.
Summary of formulas used for net price in a series of discounts and for calculating the single discount rate equivalent.
Importance of understanding trade discount series for businesses to strategically price products and manage discounts.
Practical application of trade discount calculations in retail and wholesale businesses to determine final prices and savings.
Transcripts
good day our topic will be trade
discussed so the alpha
will be the following so we have
definition of terms
as well as derivation of formula and the
stated
samples
okay so let's have suggested retail
price catalog price this price
mean all the same thing so meaning to
say the price which the manufacturer
suggests an item to be sold
to the customers
well the trade is gone it is the amount
of discount that the wholesaler or
retailer receives of
the list price so this is the difference
between the list price
and the net price
so let's have next which is net price
so the net price is actually the price
of an apache
or retainer piece for the list price
minus the trade
disk
next our definition of term is actually
the discount rate
so it is the amount of item to be paid
by the retailer to the manufacturer
so let's talk about the formula that we
will use for this trade discount so
let's have first the trade discount
so the trade discount is equal to the
product of discount rate and the list
price
so if we will put this in symbol so td
is equal to dr
times lp where in td is the trade
discount
dr is the discount rate and lp is the
list price
next on our formula is the net price so
we have
okay so net price is actually the list
price minus trade discount
okay we are in symbol np is equal to lp
minus td
such that np is the net price lp is the
list price and td is the trade discount
or i can rewrite this one as np
is equal to lp minus dr times lp
take note that the trade discount is
equal to the discount rate times the
list price
and powering the common buffer which is
after the lp
so i have the net price is equal to this
price times 1
minus er okay
let's have our example an item listed at
10 000 pesos
is subject to a discount of 20 percent
so what is the amount of discount
and the net price so let's have our step
number one but before that
let's identify first the given since our
given is ten thousand so that is
considered as the list price
and twenty percent as our discount print
so let's have step number one so we
would like to find the trade discount
take note that the trade discount is
equal to list price times discount three
then we will plug
in the numbers so this price is equal to
ten thousand
and our discount rate is twenty percent
but take note we will convert twenty
percent into decimal first
so we have ten thousand times point
twenty or the final answer for
three discount is equal to twenty
thousand
so this is your trade discount or
simply ask the discount next we want to
find out the net price
so we will move on to the second step so
that is why
find the net price so to find for the
net price that is after the list price
minus the trade discount take note that
our list price is equal to ten thousand
while our trade discount
or simply as the discount is equal to
two thousand
so we have net price is equal to eight
thousand pesos so therefore the discount
is two thousand pesos
and the net price is eight thousand
pesos
that's our second example the mpd
factory sold 20 000 pesos
water flows to the kog store the given
amount represents the retail price
of the votes for which the npd factory
has offered a 15 percent
rate this discount what is the apple
amount trade of kyj store
and what is the late discount now in
order to solve this problem let's
identify first the
given since the list price is equal to
20 000 pesos
discount rate is 15 we do not know yet
the net price as well as the trade
discount
since we do not know the trade discount
yet
let's look for the net price but they
told that we can use the formula
net price is equal to this price times 1
minus discount rate
since we do not know the rate discount
so since the list price is equal to 20
000
and the discount rate is feels 15
so i can simply plug in the numbers so i
have twenty thousand
times one minus fifteen percent
or twenty thousand times eighty five
percent
then i'll convert eighty five percent to
decimal
so i have 20 000 times 0.85
or the net price is equal to 17 000
pesos
since i know not the net price then i
can determine now the trade is gone
so that is my second step so the trade
discount is equal to this price
minus the net price take note that the
list price is equal to twenty
thousand minus seventeen thousand
so the trade discount is equal to three
thousand
pesos so the amount paid by kyj store
is seventeen thousand pesos and the
trade discount is three thousand pesos
let's move on to the next example so
what is
the discount rate if the net price of an
item is 7500 vessels
after giving a discount of 2500
so before we solve this problem let's
identify
the cuban so take note that the net
price is equal to 7500
while the trade discount is 2500
but we do not know the least price as
well as the discount rate
so we want to find out first that is
price
now take note in order to find the list
price
that is actually net price plus the
trade discount
then we will plug in the numbers of
7500 plus 2500
so the list price is equal to 10 000
pesos next we want to find out the
discount rate
now in order to find the discount rate
we'll start with the formula of
discount or trade discount is equal to
list price
times discount rate but take note that
trade discount is equal to 2500
while the list price is equal to ten
thousand and
unknown discount rate so if we will
divide both sides of the equation by
ten thousand so we will have discount
rate is equal to two thousand five
hundred
divided by 10 000 so the discount rate
is equal to 0.25
or this country is equal to 25
so there are four so the discount rate
is
25 percent
to summarize our list of uh formula so
we have trade discount is equal to this
price times discount rate
while the net price is equal to this
price minus straight discount
trade discounts are often listed in a
series this means that a manufacturer
open these two or more trade discount
percentages
which may apply to the same this price
so this
is what we call trade discount series
here are the reasons for using discount
series
so number one is to okay encourage
volume purchases
the other one is also to promote special
or
seasonal items and finally to entice new
clients
three discount series or chain discount
it means that
it is additional discounts that are
deducted one
after another from the list price
take note that the single equivalent
rate
of discount is not simply the sum of the
individual discounts
let's have our example number one our
departure
offers a refrigerator of 25 000 pesos
plus trade discounts of 30 20
and 10 so what is the net price
also how much is the trade discount and
finally
what single trade discount is equivalent
to the series of discount
so let's have our stat number one so we
want to find out or we would like to
compute the net price
applying the trade discount of 30 take
note that
in our given so the list price is equal
to 25 000 pesos
and the discount rate is 30 percent
and we would like to find the net price
so we will apply the formula of this
price times 1 minus discount rate
and we will plug in the list price of 25
000
and the discount rate of 30 so we come
up with 25 000 pesos times 70
so we come up with the net price of 17
500 pesos so this is applying
the trade discount of 30 but take note
you still have 20 and 10
so next compute the net price applying
the trade discount of 20
so this time our list price is
17 500 while the discount rate is 25
20 so we would like to find out the net
price
now so again we will apply the net price
is equal to this price times one minus
discount rate
such that our list price now is equal to
seventeen thousand five hundred
times one minus twenty percent
so we have seventeen thousand five
hundred times eighty percent
this time our net price is 14
500 applying the trade discount
of 20 so this is your net price
next we still have the 10 discount
so step number three compute the net
price
applying the trade discount of 10
so this time our list price is actually
14 000 pesos
and the discount rate is ten percent
so we want to find out the net price
again we will plug in the formula of
this price times one minus
the discount three
so our list price now is fourteen
thousand times one
minus ten percent so we have now
talking fourteen thousand times ninety
percent
or the net price is twelve thousand
six hundred pesos so applying the thirty
percent
twenty percent and ten percent so the
net price of twenty five thousand pesos
is now twelve thousand six hundred
pesos okay next we want to find out
now the trade discount
such that the given or the list price is
actually 25 000 pesos
and the net price is actually 12 600
pesos
so using the formula of trade discount
is equal to this price
minus the net price so we have here
25 000 pesos minus twelve thousand six
hundred
so we have the trade discount of twelve
thousand four hundred pesos meaning to
say
this is the amount to save applying
thirty percent twenty 20 and 10
series of trade discount
next
we want to find out also the single rate
of the trade discount
so the list price is 25 000 pesos
while the trade discount is 12 400 pesos
so in order to find the discount rate
so let's recall that trade discount
all over the list price is equal to
discount rate
and plug in the numbers of 12 400
divided by 25 000 pesos
so we have now the discount rate of 49.6
percent
so single rate equivalent to 30
20 and 10 is 49.6 percent
so let's have the formula that we will
use for the net price in a series of
discounts so we have net price is equal
to least price
times 1 minus discount rate 1 times 1
minus the
discount rate 2 times 1 minus discount
rate 3
until 1 minus discount rate
n for the single rate equivalent so we
have
sre is equal to 1 minus the quantity 1
minus discount rate 1
times the quantity 1 minus discount rate
2
times the quantity 1 minus this country
until
the quantity 1 minus discount rate sub n
let's apply the formula based on the
previous
example so we will focus on the two
questions namely
what single three discount equivalent to
this serious
uh discount and what is the net price
so let's focus first on what is the net
price so again so the given are 25 000
for the list price
discount rate one is 30 discount rate 2
is 20
and discount rate 3 is equal to 10
now since our formula now is
net price is equal to this price times 1
minus discount rate one
times one minus discount rate two times
one minus discount rate three
and until one minus discount rate
and so on but we will focus on the three
discounts
namely 30 20 and 10
so we'll come up with net price is equal
to 25
times 70 times 80 times
90 so using our calculators and the net
price
is equal to 12 600
pesos next
we would like to find out what is the
single tree discount equivalent
again so the given r
this discount rate 1 is 30 this country
2 is 20 discount rate 3 is 10
so applying the formula so we have 1
minus discount rate
1 times 1 minus discount rate 2
times 1 minus discount 3 3. so we will
focus
only on the 3 discount rates so namely
30
20 and 10 so we have here one
minus the product of seventy percent
eighty percent
and ninety percent so using our
calculator
so the single trade discount rate
equivalent is forty nine point six
percent
so the single trade discount equivalent
is 49.6
let's have another example a new model
of cell phone is 40 000
five hundred pesos subject to fifteen
percent discount
twenty percent discount and five percent
discount
so what is the single rate equivalent so
again we will identify the given
so the least price is equal to forty
thousand five hundred pesos
discount rate one is fifteen percent
this country two is twenty percent
and discount rate three is five percent
so we will plug into this
away these numbers to our formula such
that the single rate equivalent
is equal to one minus one minus discount
rate one
times one minus discount rate two times
one minus discount rate three and so on
but we have only three discount rates so
we have here
1 minus 1 minus 15
times 1 minus 20 percent times 1 minus 5
so we will come up with 1 minus the
product of 85 percent
80 percent and 95 so we will come
up with a single rate discount
equivalent of 35.4
so we can say that the single rate
equivalent of
15 percent 20 and 5
respectively is equal to 35.4
using the same problem from the previous
example
so a new model of cell phone is forty
thousand five hundred
subject to fifteen percent twenty
percent and five percent discount
so this time we would like to find out
the net price
so what is the net price so given that
our
list price is equal to forty thousand
five hundred
and the single rate equivalent or the
discount rate
is equal to thirty five point four
percent now
so we can apply the formula of net price
is equal to this price times one minus
discount rate
okay take note that the single rate
equivalent is now equal to discount
three
so plug in the numbers so we have here
this price is equal to forty thousand
five hundred times one minus thirty five
point four
percent based on the previous
computation
so we have here now that price is equal
to twenty six thousand
one hundred 163
so the net price is 26
163 pesos
again using the same example in number
two
so a new model of cell phone is forty
thousand five hundred
subject to fifteen percent twenty
percent and five percent discounts
so this time we want to find out the
trade discount
so if we are talking about the trade
discount this is the summation now
of 15 20 and 5
respectively again so the list price is
equal to 40
500 well this time the net price is 26
163 based on the previous computations
so take note that the trade discount is
equal to list price
minus the net price so 40 thousand
hundred minus twenty six thousand one
hundred sixty three
so the trade discount is equal to
fourteen thousand three hundred
thirty seven it means that this is the
total discounts
that you can save from 40 500
applying the 15 20 and 5
discounts so therefore so trade discount
is 14
337 pesos
to summarize our discussion in the
series of discounts so the net price
is equal to this price times 1 minus
discount rate 1
times 1 minus discount rate 2 times 1
minus discount rate 3
until and so on and so forth for the
single 3 discount rate equivalent
or we can rename this one a single
discount equivalent
so it has a formula of 1 minus
as a quantity 1 minus discount rate 1
times 1 minus discount rate 2
times 1 minus discount rate 3 and so on
and so forth
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