Welcome!
In this video, we discuss discount series or multiple discounts, or what is also called
chain discounts.
We explore the relationship between net price, list price,
and the amount of discount when multiple discounts are offered,
and also calculate the single equivalent rate of these discounts.
Suppose a store is offering a 20% discount on an item but the store also offers an additional
25% discount to students when they present their student cards.
Our goal is to combine these two discount rates into a single rate.
You might think, “that’s easy, 20+25 = 45.
The single discount rate is 45%.”
But that would be incorrect.
The discount rates should not be added but applied in succession, one after the other.
Consider this: A student walks in to the store to purchase
an item listed at $100.
On applying the 20% discount, $100 minus 20% will yield a net price of $80.
And for the second discount, $80 minus 25% will yield a net price of $60.
That is, the two discounts yield a net price of $60, which is 60% of the $100 list price.
So, the student ends up getting a $40 discount which is 40% of the $100 list price.
In essence, the single equivalent rate of discount for the discount series of 20% and
25% is 40%, and not 45%.
Recall that the 20% discount means that the student pays 80% or 0.8 of the list price,
while the 25% discount means that the student pays 75% or 0.75 of the already reduced list
price.
Note that it does not matter which discount is applied first (the 20% or the 25%), the
final net price remains the same.
Thus, we have a net price formula for the discount series as
Net Price = (1 – discount rate 1) times (1 – discount rate 2) times the List Price.
That is, N = (1 – d1)(1 – d2)L. And that can be extended to cases with 3 or
more discounts.
Now, recall that the student paid 60% of the list price.
That is, 0.8*0.75 = 0.6.
Therefore, the single rate of discount is 1 – 0.6, which equals 0.4 or 40%
The single equivalent rate of discount can thus be calculated by using this formula:
de = 1 – [(1 – d1)(1 – d2)] which can also be extended to 3 or more discounts.
Now, let’s solve some problems:
In number 1, we have a discount series of 20%, 10% and 8% with a list price of 840.
To calculate the net price, we can use the net price formula with 3 discount rates.
And substituting the values will give a net price of $556.42.
Now, the amount of discount is the difference between the list price and the net price.
So, we subtract the net price from the list price.
And that will give 283.58.
To find the single equivalent rate of discount, we can simply divide the amount of discount
by the list price to obtain 33.76%.
Alternatively, we can also use the single equivalent rate of discount formula to obtain
the same result.
It is important not to round the results till we obtain the final answer here.
In number 2, we want to calculate the list price after a discount series of 12.5% and
10% yields a net price of $82.69.
We now substitute the values into the net price formula for 2 discount rates.
And that will give 82.69 equals 0.7875L Dividing both sides by .7875 gives a list
price of $105.
And that’s it.
Thanks for watching.