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CHAPTER 4
MATHEMATICS OF BUYING
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4.1 Invoices and Trade Discounts
4.1.1 Invoice

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Invoice – a printed record of a purchase or
sale
Sales invoice – records a sale
 Purchase invoice – records a purchase


Extension total – the number of items purchased
times the price per unit, any discounts, the shipping
and insurance charges.

Invoice total – the sum of all the extension
totals.

Total invoice amount – same as invoice total
excluding shipping
and insurance.
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
Common shipping terms:
 Free on Board (FOB) shipping point or
destination – seller pays for shipping to
this destination. Beyond this point, the
purchaser pays for shipping.
Seller pays
shipping and
insurance
FOB
shipping
point
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Buyer pays
shipping and
insurance
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
Invoice terms:

Trade discount: offered to businesses who
buy an item that is to be sold.

List price: suggested price at which the
item is to be sold to the public.

Net price: the amount to be paid by the
buyer.

Net price = List price – Trade discount
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Example of an invoice:
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Example of an invoice:
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4.1.2 Trade Discount

Trade discount is a reduction from the list
price offered by wholesalers to retailers so
that they can re-sell the merchandise at a
profit.

The amount of discount that retailers receive
from wholesalers is known as trade discount
amount.
−
Trade discount = List price – Net price
−
Formula:
NP = L (1 – r)
Where:
NP = Net price
L = List price
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r = trade discount
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Example 1:
The list price of a personal desktop is RM 2599. A
trade discount of 15% is offered. What is the net
price of the personal desktop?
Solution:
List price = RM 2599
Trade Discount = 15% x RM 2599
= RM 389.85
NP = List price – Trade discount
= RM 2599 – RM 389.85
= RM 2209.15
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Example 2:
USPD offers a discount of 10% on all the model of
cars it sells. What is the net price of a Proton
Savvy that is listed at RM 56490?
Solution:
NP = RM 56490 (1 – 0.1)
= RM 56490 (0.9)
= RM 50841
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Example 3:
A bill of RM 3500 including a prepaid handling
charge of RM 250 is offered a trade discount of
17%. What is the net price?
Solution:
List price = RM 3500 – RM 250 = RM 3250
NP = RM 3250 (1 – 0.17)
= RM 3250 (0.83)
= RM 2697.50
*(It should be noted that the discount is based on
the cost of goods, excluding any other cost)
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4.3 Chain Discount
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
A trade discount in a series of two or more
successive discounts.

Wholesaler lists the chain discount as a
group, for example 15%, 10%, 5%.

These discounts might also be given in
circumstances such as when a large quantity
is ordered.
−
Formula:
NP = L(1 - r1) (1 – r2) (1 – r3)
Where:
NP = Net price
L = List price
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Example:
A jeans is advertised for RM 280 less 10% and
5%. Find,
a) The net price,
b) The total discount.
Solution:
a) NP = L(1 - r1) (1 – r2)
= RM 280 (1 – 0.1) (1 – 0.05)
= RM 280 (0.9) (0.95)
= RM 239.40
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b) Total discount = RM 280 – RM 239.40
= RM 40.60
*(It should be noted that the chain discount of 10%
and 5% is not the same as 15%)
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4.4 Single Discount Equivalent
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
A single discount equivalent is a single
discount which is equivalent to a chain
discount.

The single discount equivalent, r for a chain
discount of r1, r2 and r3 is given by:
r = 1 – (1 - r1) (1 – r2) (1 – r3)
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Example:
A pair of shoes is advertised at RM 229 less 15%,
10% and 5%. Find,
a) The single discount equivalent,
b) The net price.
Solution:
a) r = 1 – (1 - r1) (1 – r2) (1 – r3)
= 1 – (1 – 0.15) (1 – 0.1) (1 – 0.05)
= 1 – (0.85) (0.9) (0.95)
= 1 – 0.72675
= 0.27325 = 27.325%
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b) NP = L (1 – r)
= RM 229 (1 – 0.27325)
= RM 229 (0.72675)
= RM 166.43
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4.5 Cash Discount
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
Cash discounts are often stated under the
heading of invoice as, for example 3/10, 2/20,
n/30.

This means, if the buyer pays the invoice
within 10 days of the invoice date, the buyer
is entitled to receive a 3% discount or, if
payment is made within 20 days from the
invoice date, the buyer will receive a 2%
discount.

N/30 (sometimes written net 30) means the
credit period is 30 days.
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Example:
An invoice dated 15 November 2007 for RM 2800
was offered cash discount 2/10, 1/15, n/30. If the
invoice was paid on 27 November 2007, what was
the payment?
Solution:
15 Nov – 27 Nov = 12 days, so entitle for a 1%
cash discount
Net Payment = NP – Cash Discount
= RM 2800 – (0.01 x RM 2800)
= RM 2800 – RM 28 = RM 2772
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4.6 Partial Payment of Invoice

If a buyer pays only part of the invoice within
the discount period, he receives a
proportionate fraction of the cash discount
that is offered.

He will only receive the full amount of the
cash discount if he settles all the payment.
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Example:
An invoice amounting to RM 4500 and dated
27 October 2007 offered cash discount terms of
10/15, n/30. Find the amount outstanding if the
buyer paid RM 2000 on 5 November 2007.
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Solution:
Amount paid = (Credit given) x (1 – Discount rate)
RM 2000 = (Credit given) x (1 – 0.1)
Credit given = RM 2000
0.9
= RM 2222.22
Outstanding amount = RM 4500 – RM 2222.22
= RM 2277.78
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