Welcome. In this video
we now extend the relationship between the List Price, and the Trade Discount to the Net Price.
The Net Price is the actual amount paid after the discount has been applied.
That is, the Sale Price.
So, the Net Price = List Price – Amount of Discount.
Or N (Net Price) = L minus uppercase D.
Since the Amount of Discount is rate of discount times List Price, the net price can also be
represented as L times (1 minus d)
1 minus d here is the rate that is actually paid.
For example, if the rate of discount is 40%, d = 0.4, then 1 minus d equals 0.6.
And the customer is paying 60% of the list price.
1 minus d is thus the complement (or the opposite) of the discount percent.
We can again use this visual aid to remember the relationship.
N is L times (1 - d) L equals N over (1 - d)
And (1 - d) is N over L Now, let’s look at some questions:
In the first question, we need to calculate the net price when the List Price is 2400,
and “less 8%” here means that the discount rate is .08.
Substituting that in the net price formula gives 2208.
So, 8% discount here means that 92% of the list price is the net price.
On most calculators, like the BAII plus, you can simply input 2400 minus 8%, and then the
equal sign to obtain 2208.
In number 2, we want to calculate the list price given the rate of discount is 16 2/3%.
To convert that to decimal, we first divide 2 by 3 to get 0.666… repeating.
We the add 16 to it, and divide by 100.
So, the rate of discount is 0.166… repeating.
Note that we do not just round this value to 0.17.
Doing so will result in loss of accuracy.
We should make sure we use all the decimal places the calculator can handle when working
with repeating decimals.
The Net price is 2550 since that’s the amount the item sold for.
The list price is thus calculated as 2550 over 0.8333… repeating.
And that gives $3,060.
In number 3, we want to calculate the net price if the rate of discount is 12.5% and
the amount of discount is $72.
That is, d = 0.125 and D = $72.
Since the List price is not given here, we cannot calculate the net price directly, using
our formula.
We can, however, find the List price using the relationship we derived earlier.
That is, the List price equals Amount of Discount divided by the rate of discount.
So, the List price equals 72 over .125 which gives $576.
We can then find the net price by simply subtracting the amount of discount from the List Price.
And that gives $504.
In number 4, we want to calculate the rate of discount, given a list price of $399.99
and a Net Price of $347.99 . Here, since we have both Net Price and List
Price, we can solve for the rate of discount in the net price formula if we want.
We can also easily first find the amount of discount by subtracting the net price from
the list price.
And that gives $52.
And then find the rate of discount by dividing the amount of discount by the list price.
And that gives 13%.
And that’s it.
In the next set of videos, I will be going over multiple discounts, markups, and markdowns.
Thanks for watching.