1. QMT 3301 BUSINESS MATHEMATICS
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CHAPTER 4
MATHEMATICS OF BUYING
QMT BUSINESS MATHEMATICS

2. 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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3. Seller pays shipping and insurance Buyer pays 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.
FOB shipping point
Seller pays shipping and insurance
Buyer pays shipping and insurance
QMT BUSINESS MATHEMATICS

4. QMT 3301 BUSINESS MATHEMATICS
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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
QMT BUSINESS MATHEMATICS

5. QMT 3301 BUSINESS MATHEMATICS
Example of an invoice:
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6. QMT 3301 BUSINESS MATHEMATICS
Example of an invoice:
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7. QMT 3301 BUSINESS MATHEMATICS
4.1.2 Trade Discount
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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
r = trade discount
QMT BUSINESS MATHEMATICS

8. QMT 3301 BUSINESS MATHEMATICS
Example 1:
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The list price of a personal desktop is RM 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
NP = List price – Trade discount
= RM 2599 – RM
= RM
QMT BUSINESS MATHEMATICS

9. QMT 3301 BUSINESS MATHEMATICS
Example 2:
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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 (1 – 0.1)
= RM (0.9)
= RM 50841
QMT BUSINESS MATHEMATICS

10. QMT 3301 BUSINESS MATHEMATICS
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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
*(It should be noted that the discount is based on
the cost of goods, excluding any other cost)
QMT BUSINESS MATHEMATICS

11. QMT 3301 BUSINESS MATHEMATICS
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
QMT BUSINESS MATHEMATICS

12. QMT 3301 BUSINESS MATHEMATICS
Example:
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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
QMT BUSINESS MATHEMATICS

13. QMT 3301 BUSINESS MATHEMATICS
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b) Total discount = RM 280 – RM
= 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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14. 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)
QMT BUSINESS MATHEMATICS

15. QMT 3301 BUSINESS MATHEMATICS
Example:
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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 –
= = %
QMT BUSINESS MATHEMATICS

16. QMT 3301 BUSINESS MATHEMATICS
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b) NP = L (1 – r)
= RM 229 (1 – )
= RM 229 ( )
= RM
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17. QMT 3301 BUSINESS MATHEMATICS
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.
QMT BUSINESS MATHEMATICS

18. QMT 3301 BUSINESS MATHEMATICS
Example:
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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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19. 4.6 Partial Payment of Invoice
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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.
QMT BUSINESS MATHEMATICS

20. QMT 3301 BUSINESS MATHEMATICS
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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.
QMT BUSINESS MATHEMATICS

21. QMT 3301 BUSINESS MATHEMATICS
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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
Outstanding amount = RM 4500 – RM
= RM
QMT BUSINESS MATHEMATICS