Discount is merely an illusion used by businessmen .Argue this statement either in support or against it with reference to the mathematical concept of discount
Answers
TRADE DISCOUNT
A trade discount is an amount deducted from the list price. It is the product of the discount rate
and the list price. The list price is the suggested retail price determined by the manufacturer or
distributor and listed in their product list or catalogue.
Amount of discount = Rate of discount × List price
For example, if a textbook lists for $40 and is discounted 20%, the discount is:
Discount = 20% × $40 = 0.2 × 40 = $8
[Hint: Remember to change the percent to a decimal number before multiplying]
The actual or the net price is the difference between the list price and the amount of discount. It
is also sometimes called the sale price.
Net price = List price − Amount of discount
In the case of the textbook: Net price = $40 − $8 = $32
Example: A pair of jeans that originally cost $90 is now on sale for 30% off. What is the (a) the
amount of discount, and (b) the net price.
Solution: (a) Amount of trade discount = 0.30 × $90 = $27
(b) Net price = $90 − $27 = $63
Instead of computing the amount of discount and then deducting this amount from the list price,
the net price can be found using the net factor approach. The Net Price Factor (NPF) or net
factor can be found using the following formula:
Net Price Factor (NPF) = 100% – % discount
NPF = 1 – d
The relationship between net price and list price may be stated generally as:
Net Price (N) = Net Price Factor (NPF) × List Price (L)
N = (1 – d) × L or N = L × (1 – d)
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes. 2
Example: Find the net price for list price $30 less 30%.
Solution: Net price = L × (1 − d) = 30 × (1 − 0.30) = 30 × 0.70 = $21
DISCOUNT SERIES (MULTIPLE DISCOUNTS)
Sometimes sales people offer several discounts to entice the customer to buy the product. If a
list price is subject to two or more discounts, these discounts are called a discount series.
The key thing to understand about multiple discounts is that the second and third discounts are
not based on the original price. They are based on the already discounted price. The short-cut
equation to calculate net price in a discount series is given as:
Net Price = (NPF of 1st discount) × (NPF of 2nd discount) x List Price
N = (1 − d1) × (1 − d2) × L
If there are more than 2 discounts;
N = (1 − d1) × (1 − d2) × (1 − d3) …..(1 − dn) × L
Example: An item listed at $100 is subject to the discounts of 20%, 10% and 5%.
Determine the net price.
Solution: N = (1 − d1) (1 − d2) (1 − d3) L
N = (1 − 0.2) (1 − 0.1) (1 − 0.05) × $100
N = (0.684) × $100 = $68.40
When you are dealing with a series of discounts you almost always want to know what the
actual rate of discount really is. This is referred to as the Single Equivalent Discount (SED).
The formula to calculate SED is:
SED = 1 − NPF for the discount series
SED = 1 − [(1 − d1) × (1 − d2) × (1 − d3) …..(1 − dn)]
For the discount series in example 3, the SED = 1 – 0.684 = 0.316 or 31.60%
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes. 3
Practice Problems
1. A 30% discount on a stereo amounts to $45.58. Compute the list price and the net price.
2. Frank’s Décor sells curtains for $85.85 less 25%. What additional discount percent must the
store offer the meet a competitor’s price of $50.65?
3. A BBQ grill is listed for $520.75 less 10%, 5%, 2%.
(a) What is the net price?
(b) What is the total amount of discount allowed?
(c) What is the exact single rate of discount allowed?
4. Fill in the blanks for the following categories:
No. Rates of discounts List Price Net Price SED
a. 10%, 15% 105.60
b. 33⅓%, 5%, 7% 54.74
c. 25%, 10%, 10%, 5% 15.25
Solutions
1. List Price = D/d = $45.58/0.3 = $151.93
Net Price = L − D = $151.93 − $45.58= $106.35
2. Net Price = (1 − d) × L = 0.75 × $85.85 = $64.39
Additional discount = $64.39 − $50.65 = $13.74
Additional discount percent = 13.74/64.39 = 21.34%
3. (a) N = (1 − d1) (1 − d2) (1 − d3) × L
N = (1 − 0.1) (1 − 0.05) (1 − 0.02) × $520.75 = (0.8379) × $520.75 = $436.34
(b) D = L − N = $520.75 − $436.34 = $84.41
(c) SED = 1 − [(1 − d1) (1 − d2) (1 − d3)] = 1 − 0.8379 = 0.1621 or 16.21%
4.
No. Rates of discounts List Price Net Price SED
a. 10%, 15% 105.60 80.78 23.5%
b. 33⅓%, 5%, 7% 92.94 54.74 41.1%
c. 25%, 10%, 10%, 5% 26.42 15.25 42.29%
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes. 4
CASH DISCOUNT
Many manufacturers and wholesalers allow customers to take a cash discount, a reduction of
the amount due on an invoice to encourage prompt payment of the bill. Calculating the cash
discount can be tricky since you need to know how to count the exact number of days for which
the discount is offered. Knowing if a month has 30 or 31 days (or 28 in the case of February) is
important.