Lesson 2 6.1 Trade Discount Series winter 2021 PDF

Preview

Summary

Lesson 2 6.1 Trade Discount Series winter 2021...

Description

LESSON 2 (SECTION 6.1) TRADE DISCOUNT SERIES A manufacturer may offer two or more discounts to different members of the supply chain. Example An item listed at $150 is subject to trade discounts of 20%, 10%, 3%.

Company A is only entitled to the 20% discount. Find the net price. N = L(1− d ) = 150(1− 0.2) = $120

Company B is entitled to the 20% and the 10% discounts. Find the net price. N = L(1− d ) = 120(1− 0.1) = $108

Company C is entitled to all three discounts of 20%, 10%, 3%. Find the net price. N = L(1− d ) = 108(1− 0.03) = $104.76

Or N = 150(1− 0.2)(1− 0.1)(1− 0.03) = $104.76 Note for the discount series 20%, 10%, 3%, do not add the discounts.

When there are three discounts, there are three discounting factors. The formula for net price is

N = L(1− d1)(1− d2 )...(1− d n ) 1

LESSON 2 (SECTION 6.1) TRADE DISCOUNT SERIES Example Which choice is better for the buyer, to receive the discount series 20%, 10%, 3% or a single discount of 31%? In the above example, the net price is $104.76 Using a single discount of 31%, N = 150(1− 0.31) = $103.50 Therefore, a single discount of 31% is better for the buyer because is results in a lower net price. Example What single discount is equivalent to the discount series 20%, 10%, 3%? Using the example above, L = 150, N = 104.76 D = 150 – 104.76 = $45.24

d = D = 45.24 = 30.16% L 150 Or Rate of change =

150 − 104.76 45.24 30.16% = = 150 150

A single discount of 30.16% is equivalent to the discount series 20% 10%, 3% Exercise 6.1 page 229 #14b) Determine the single rate of discount equivalent to the series 25%, 8 1/3%, 2% Formula d = 1− (1− d1)(1− d2 )...(1− dn ) d = 1− (1− 25%)(1− 813 %)(1− 2%) = 32.625%.

d = 32.625% is the exact value

2

LESSON 2 (SECTION 6.1) TRADE DISCOUNT SERIES

N = L(1− d1)(1− d2 )...(1− dn )

d =1−(1− d1)(1 − d2)...(1−dn )

#16 A mobile phone is listed for $174 less 16 23 % , 10%, 8% a) What is the net price? Find N

N = L(1− d1)(1− d2 )(1− d3 ) = 174(1− 16 2 3 %)(1− 10%)(1− 8%) = $120.06 b) What is the total amount of discount allowed? Find D

D = 174 −120.06 = $53.94

c) What is the exact single rate of discount that was allowed? Find d

d=

D 53.94 = = 31% or 174 L

d = 1− (1− d1)(1− d 2 )...(1− dn ) = 1− (1− 162 3 %)(1− 10%)(1− 8%) = 31% 3

LESSON 2 (SECTION 6.1) TRADE DISCOUNT SERIES #24 What is the list price of an article that is subject to discounts of 33 1/3%, 10% and 2%, if the net price is $564.48?

Solution

Solve the formula for L

N = L(1− d1)(1− d 2)...(1− dn )

L=

=

N

(1− d1 )(1− d2 )...(1− dn )

564.48 (1− 33 13 % )(1−10% )(1− 2%)

= $960

The list price is $960.

4

LESSON 2 (SECTION 6.1) TRADE DISCOUNT SERIES Additional Rate of Discount #20 An office desk listed at $440 less 25%, 15% is offered at a further reduced price of $274.89. What additional rate of discount was offered? Solution We could solve for d3 in the formula N = L(1− d1)(1− d2 )...(1− dn ) It would be easier to solve this problem in two steps Step 1 Find the net price after the two discounts of 25%, 15%

N = 440(1− 25%)(1− 15%) = $280.50 Step 2 Find d 3 that will reduce $280.50 to $274.89. Express this change as a percent.

Using the rate of change d3 =

5.61 280.50 −274.89 = 2% = 280.50 280.50

To check your answer,

N = 440(1− 25%)(1−15%)(1−2%) = 274.89 Therefore, the additional rate of discount is 2%

5

LESSON 2 (SECTION 6.1) TRADE DISCOUNT SERIES Additional Rate of Discount #22 A computer listed at $1260 less 33 13 % and 16 2 3 % is offered at a clearance price of $682.50. What additional rate of discount was offered?

Solution Step 1 Find the net price after the two discounts of 33 1/3%, 16 2/3%%

N =1260(1− 33 13%)(1−16 23%) = $700

Step 2 Find d3 that will reduce $700 to $682.50. Express this change as a percent.

Using the rate of change

d 3 = 700 − 682.50 = 17.50 = 2.5% 700 700

The additional rate of discount that was offered is 2.5%

6

LESSON 2 (SECTION 6.1) TRADE DISCOUNT SERIES Additional Rate of Discount

#28 Polar Bay Wines advertises California Juice listed at $125 per bucket for a discount of 24%. A nearby competitor offers the same type of juice for $87.40 per bucket. What additional rate of discount must Polar Bay Wines give to meet the competitor’s price? Step 1 Find the net price for Polar Bay Wines.

N = 125(1− 24%) = $95

Step 2 Polar Bay Wines wants to further reduce its net price of $95 to $87.40 to meet the competitor’s price. Express this change as a percent.

d3 =

95 − 87.40 7.60 8% = = 95 95

Polar Bay Wines must offer an additional discount of 8% to meet the competitor’s price of $87.40.

7

LESSON 2 (SECTION 6.1) TRADE DISCOUNT SERIES Homework Exercise 6.1 pages 228-230 Practice Problems #13-27 odd numbers Online Study Plan

8...