Consumer Arithmetic

CONSUMER ARITHMETIC

By: Kasskassmaths​

​General Mathematics Syllabus

Section #2 , Objectives ​1 - 10

TABLE OF CONTENTS

Discount - Slide 3

Sales Tax (VAT) - Slide 5

​Percentage Profit & Loss - Slide 6

Hire Purchase - Slide 7

Mortgage - Slide ​9

Simple Interest - Slide 10

Compound Interest - Slide 12

Appreciation Slide 13

Depreciation - Slide 14

Currency Conversion - Slide 15

Rates and Taxes - Slide 16

​

​

​Salary and Wages - Slide 21

​Electricity Bill Slide 26

Telephone Bill Slide 29

Invoices and Shopping Bills​ - Slide 31

Insurance and Investment - Slide ​33

Past ​Paper Questions to practice - Slide 36

Discount

Egs.

2. In a sale a recorder was sold for $2071, after a discount of 5% was given. Calculate the SP of the recorder.

SALEX TAX (VAT)

VAT = 12.5% (or 15%)

VAT price = 12.5 % x price of item

VAT inclusive = Price ​of item + VAT price

Eg. The price of a steamer without VAT is $3473. Calculate the price of the steamer VAT inclusive if the VAT charged is 12.5%.

​

​

​VAT inclusive = $3473 + $434.13

= $3907.13​

PERCENTAGE PROFIT AND LOSS

​E.g. A shop keeper buys 25 balls at a total cost of $150.

a) He sells them for $8 each, what is the percentage profit.

b) He ​sells them for $5 each, what is the percentage loss.

​a) SP = 25 x 8 = $200

P = SP - CP

= 200 - 150

= $50​

​b) SP = 25 X 5 = $125

L = CP - SP​

Loss = 150 - 125 ​

= $25​

HIRE PURCHASE (HP)

Hire Purchase = downpayment + amount payable

Amount payable = outstanding balance + interest

Note : These 2 equations can be rearranged to find another​.

E.g. The marked price of a TV set is $6980. If the customer pays cash, then the price is 12% below the marked price. If the set is bought on HP then the buyer pays a downpayment of $628.20 and 24 monthly installments of $344.06 each. a) Determine CP.

b)The HP price.

c)The difference between HP& marked price.

d)the percentage interest charged on the outstanding balance.

​

Answers

​b) HP = 628.20 + (24 x 344.06)

= 628.20 + 8257.44

= $8885.64​

​c) HP - SP

= 8885.54 - 6980

​= $1905 .64

​d) outstanding balance
= amount payable - interest

= 8257.44 - 1905.64

= 6351.80

​

Mortgage

Interest payed =

amount payed to bank - amount borrowed

​

E.g A house costing $150 000 can be bought by making a 10% deposit and taking a bank mortgage.

a) calculate the deposit

b) the amount borrowed

c) total amount payed to the bank if monthly payments of $2250 are made over a 20-year period

d) the amount of interest payed to the bank

e) total amount payed for the house ​

​b) Amt borrowed =
150 000 - 15000 = $ 135000​

​c) Amt payed =
2250 x (20 x 12) = $540 000​

​d) Interest payed =
540 000 - 135 000 = $ 405000​

​e) total =
540 000 + 15 000 = $ 555000​

SIMPLE INTEREST

E.g.

Ms Laws borrowed $10 000 from a bank and a simple interest rate of 8% per annum for 3 years.

a) What amount is the SI payable?

b) Calculate the amount accruing for the loan.

c) Deteremine the amount of each monthly installment. ​

COMPUND INTEREST

APPRECIATION

DEPRECIATION

​b) D = P - A

= $27 000 - $23149.13

= $ 3850.87​

CURRENCY CONVERSION

Depending on the rate of exchange, to change one currency to another, division or multiplication (not both) will be the operation used.

​US $1.00 = $TT6.30

US$1000 = 6.30 X 1000

= $ 6300 TT​

​b) The Tourist spent TT $4200 while vacationing and converted the remained into Canadian Currency. Calculate the amount of CAN dollars he received.

​E.gs 1) Note the following bank rates : -

​US $1.00 = TT $6.30

CAN $1.00 = TT$4.90

a) In May 2004 an American tourist changed US$1000 into TT currency. Calculate the amount of TT dollars he received.​

​TT $ remain = 6300 - 4200 = $ 2100​

Rates and Taxes

E.g The rateable value of a house in Port - of- Spain is $ 1625. Given that the rate charged by the local council for that area is 0.25cents for the $1, determine the amount of money the owner pays in rate per annum.

Answer :​
rate per annum =
rate charged x rateable value

= 0.25 x 1625

= $406.25​

WATER RATE

Mr. Adam used 105m³ of water for the first half of 2002.
In 2002 water rate for domestic users were as follows :

$2.50 per ​m³ for the first 25m³

$2.00 per m³ for the next 50m³

$1.50 per ​m³ for amounts excess of 75m³

5% discount on bills paid before July 7th.​

​Steps :
1) Determine the amount paid for the amount of water used, ​given the conditions/rates.
2) Total the amounts.​
3) Calculate and subtract any discounts or add any taxes.

​Calculate the amount MR Adams paid for half the year assuming the bill was paid before July 7th.

Answer Format

​Note :

​first 25 : 105 - 25 = 80(remain)

next 50 : 80 - 50 = 30 ​(remain)

​final remainder : 30

GAS RATE

Calculated similar to Water rate.

E.g Ms Eve used 85m³of domestic gas for the first half of 2003. In 2003, gas rates were as follows :

$0.85 per m³ for the first 30m³

$0.95 per m³ for the next 50m³

$1.05​ per m³ for amounts excess of 80m³

3% discount on bills paid before July 7th.

Govt tax of 5%

​

​Calculate the amount Ms Eve paid for half of the year assuming the bill was paid on July 4th.

​Note : it is possible to add taxes first, then remove the discount from the new amount. However, the discount is usually calculated first.

Answer format

​Note :

first 30 : 85 - 30 = 55(remain)

next 50 : 55 - 50 = 5 (remain)

​excess = 5

​

Salary and Wages

Salary : -

• gross annual sa​lary = gross monthly salary x 12

• net monthly salary = gross monthly salary - monthly deductions

• net annual salary = net month​ly salary x 12

Basic Wage : -

Basic wage = basic rate x basic week

​

​Egs. 1) Calculate the basic wage for the following factory worker :

# of hours worked = 38

basic rate = $5.40​

​basic wage = basic rate x basic week

= 5.40 x 38

= $205.20​

overtime wage

gross​ wage = basic wage + overtime wage

overtime wage = overtime rate x overtime worked​

where overtime rate are as follows :

• time and a quarter = 1.25 x basic rate

• time and a half = 1.50 x basic rate

• double ti​me = 2 x basic rate

• tripe time = 3 x basic rate

​E.g. A sales clerk is paid a basic rate of $3.75 during Christmas. She works 6 hours over time on Friday at time and a quarter. What is her overtime wage? The clerk works a basic week of 40 hours. Evaluate her basic wage and gross wage.

​overtime rate = 1.25 x 3.75

= $4.69

​

overtime wage = 4.69 x 6

=$28.14​

basic wage = basic rate x basic week

= 3.75 x 40

= $150

​

gross wage = basic wage + overtime wage ​

= 150 + 28.14

= $178.14​

Commission

E.g. A car ​salesman is paid a basic wage of $600. In addition, he's paid a commission of 1.5% of the car's total. During a certain week, he sold cars valued at $97 600 and $68 700. Calculate for that week the commission and his gross wage.

​commission = x% of the total value of the item sold

gross wage = basic wage + commission

​total cars sold = $97 600 + $68 700 = $166 300​

​gross wage = 600 + 2494.50

= $3094.50​

Electricity Bill

conversions

1kw = 1000w

1kwh = 1000wh

1kwh = 1 unit

​where : w = watt, kw = kilowatt , kwh = kilowatt per hour​

no. of kwh used ​= present meter reading(kwh) - previous meter reading (kwh)

​

Note :

Questions may have a fixed charge per kwh.

There may be different schemes / conditions when calculating the charges/determining the final bill.

Look out for discounts​

​

​

​

E.g. Charges for electricity in a country are made up of a fixed fuel charge of 0.45cents per kilowatt hour and an energy charge which is computed under the following scheme.

24cents per kwh for the first 1000 units

23cents per kwh for remaining​

​

​Meter reading	in Kwh​
present​	previous​
6403​	4175​

​Calculate

(a) The number of Kwh used.

(b) Energy charged in dollars

(c) Fuel charged in dollars.

(d) The total bill

(e)​ The final bill if a 10% discount was given

​a) no. of kwh used = 6403 - 4175

2228kwh​=

​(b)

first 1000 = 0.24 x 1000 = $240.00

remaining = 1228 x 0.23 = $ 282.44

total = $ 522.44​

​(c) fuel charge

= 2228 x 0.45

= $1002.60​

​(d) total bill

= 1002.60 + 522.44

= $1525.04

​

​(f) total bill

= 1525.04 - 152.50

= $1372.54​

Telephone Bill

Note the following in these type of questions :

the amount of time

the charge(s) per s/m/h

any fixed charge(s)​

​Location	Duration ​	Fixed Charges for 3 mins or less​	​
Japan​	5​	$​22.50	$8.75​
Puerto Rico​	2​	$8.40​	$2.95​
Utah​	3​	$20.10​	​$6.85

​E.g. In May Mr. John telephone bill was calculated from the following information.

​Monthly rental = $39.00

Rebate (return) for not working for 2 weeks = $14.50

​

Calculate his final bill for the month of May.​

Japan = $22.50 + ($8.75 x 2mins)

= $40.00

​

Puerto Rico = $8.40

Utah = $20.10

​

Total = $40 + $8.40 + $20.10

= $68.50

​

Final Bill = ($68.50 + $39.00) - $14.50

= $107.50 - $14.50​

= $93.00​

Invoices and Shopping Bills

Note :

• The price of items

• The amount of items

• The % of VAT or/and discounts

​

​E.g. The following shows a shopping bill. Calculate the total amount after VAT and discount. Only those with 'V' is charged 12.5% VAT and a 10% discount is given on the total bill.

​NEW	PAPER ​	MART​
​Items	Quantity (#​)	Price per item ($)​
Books​	6​	5.40​
Pen​	8​	2.20 V​
Files​	2​	2.00 V​
Ink​	12​	15.40​

​Ink :

$15.40 x 12

= $184.80​

​

​Books :

$5.40 x 6 = $32.40

​

​Total ​

​= $ 184.80 + $32.40 + $19.80 + $4.50

​= $241.50

​Final Bill :

​= $241.50 - $24.15

=$ 217.35​

Insurance and Investment

​Note :

• ​Construct Algebraic statements

• Solving Algebraic statements

• Represent ​% as decimals.

E.g. 6% = 0.06 and 2% = 0.02

​E.g. Abby has $ 600 which she divides between 2 savings account. One earns 5% simple interest while the other earns 3% . If she earns $25 in interest total, How much did she invest into each account.

​Let x = $ invested in account with 5% SI

and
(600 - x) = $ invested in account with 3% SI

​

5% = 0.05 , 3% = 0.03​

$ invested in account with 5% SI = $350

Therefore $ invested in account with 3% SI

= 600 - 350

= $250​

​E.g.2 Mary invested a certain amount of money at 10% interest rate and $2000 more at 12% interest rate. Her yearly interest rate is $1340. How much did she invest at each rate?

​Let x = $ invested @10%

and (x + 2000) = $ invested @12%

​

10% = 0.01 , 12 % = 0.12​

​Interest earned @10% = $5000

Therefore interested earned @12% ​

= 5000 + 2000​

​= $7000

Past Paper Questions To Practice

MAY/JUNE 2024 NO. 1(b).(d)
MAY / JUNE 2023 NO. 1 (c)
May/June 2022 No. 1 (b)

​July 2021 No. 1 (b)

​June 2019 No. 1 (b)