CONSUMER ARITHMETIC
Salary, Wages and Overtime
Some employees make a ‘flat salary’ or a fixed amount during that period such as
teachers and government employees.
While some employees are paid an hourly rate so we can calculate the amount of
money they will receive when their salaries are paid. We can also calculate their
hourly rate if we know how much they made at the end of the week or the end of
the month.
In some companies employees are offered incentives for working extra time.
One such incentive is an a higher rate per hour for these extra hours. For example the
company may pay a basic rate of $30/hour. But once the employee is working extra
hours they may be paid time and a half for those hours and as such will be paid 1.5
times their basic salary for the extra hours worked.
𝑇ℎ𝑒 𝑔𝑟𝑜𝑠𝑠 𝑎𝑛𝑛𝑢𝑎𝑙 𝑠𝑎𝑙𝑎𝑟𝑦 = 𝑇ℎ𝑒 𝑔𝑟𝑜𝑠𝑠 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 ×12
𝑇ℎ𝑒 𝑔𝑟𝑜𝑠𝑠 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 = 𝑇ℎ𝑒 𝑔𝑟𝑜𝑠𝑠 𝑎𝑛𝑢𝑢𝑎𝑙 𝑠𝑎𝑙𝑎𝑟𝑦 ÷ 12
𝑇ℎ𝑒 𝑛𝑒𝑡 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 = 𝑇ℎ𝑒 𝑔𝑟𝑜𝑠𝑠 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 − 𝑇ℎ𝑒 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑑𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑠
𝑇ℎ𝑒 𝑛𝑒𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑠𝑎𝑙𝑎𝑟𝑦 = 𝑇ℎ𝑒 𝑛𝑒𝑡 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 ×12
Compute the following salary problems.
1.
A teacher is paid an annual salary of $32 160. What is his gross monthly salary?
2.
The gross monthly salary of an environmentalist is $5149. Calculate her annual salary.
3.
The gross monthly earnings of a manager is $5875. Calculate her net annual salary
after deductions of $976 were made monthly.
4.
A quantity surveyor earns $70 740 annually. Deductions of $2016 are made each
month.
Calculate his net annual salary.
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CONSUMER ARITHMETIC
Compute the following wages problems.
1.
Robin starts work each day at
7:30am and finishes at 4:30pm. He
has a 45minute lunch break.
How many hours does he work in a
normal 5 day week?
Find his basic wage if his rate of pay
is $7.25 per hour.
2.
Mr. Rayburn starts work each day at
8:00am and finishes at 4:00pm. He
has a 30minute lunch break.
How many hours does he work in a
normal 10-day fortnight.
Calculate his basic wage if his basic
rate of pay is $8.75 per hour.
3.
A man works at the same company and his wage for a 35-hour week is $263.90.
Calculate his hourly rate of payment.
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CONSUMER ARITHMETIC
Compute the following overtime problems.
2.
An employee worked 20 hours
overtime in a certain week.
Calculate;
I.
The employee’s
overtime earnings
for the week.
II.
The employee’s total
earnings for the
week.
1.
A company pays a basic wage of
$900 for a 40 hour week. Overtime is
paid at a time and a half.
Calculate;
I.
The basic hourly rate
II.
The overtime rate
3.
A secretary works a 35-hour week for which she is paid $262.50. She works 6 hours
over-time on Saturday which is paid for at time-and-a-half, and 4 hours overtime on
Sunday which is paid for at double-time. Calculate her gross wage for the week.
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CONSUMER ARITHMETIC
Compute the following overtime problems.
4.
During a certain week, Maureen worked 9 ½ hours Monday to Friday each day,
together with 6 hours on Saturday and 4 ½ hours on Sunday. The normal working day
was 8 hours and anytime worked in excess of this was paid for at time-and-a-half with
Saturday work being paid at double-time and Sunday work being paid at triple-time.
She is paid $5.60 per hour normally. Calculate;
a. Her wage for the normal working week.
b. Her overtime wage from working from Monday to Friday
c. Her overtime wage for Saturday
d. Her overtime wage for Sunday
e. Her gross wage for the week
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CONSUMER ARITHMETIC
Commission
Another incentive that some companies use is commission. This incentive is used with
salespersons. The commission is usually calculated as a percentage of the value of
the commodities sold. Salespersons are therefore more motivated to sell because
they directly profit from the sales made by the company.
𝐶𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = % 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑠𝑜𝑙𝑑
𝐺𝑟𝑜𝑠𝑠 𝑊𝑎𝑔𝑒 = 𝐵𝑎𝑠𝑖𝑐 𝑊𝑎𝑔𝑒 + 𝐶𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛
E.g. 1 A car salesperson is paid 4% commission. How much will she receive if she sells a car
valued at $20,000.
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CONSUMER ARITHMETIC
Compute the following commission problems.
1. Amanda receives 5% commission on
her first $5000 in sales and 10% on
sales beyond $5000.
If her sales amounted to $13,000
what was her commission?
3.
2.
A man receives a monthly salary of
$3500 together with a commission
of 5% on all sales over $5000 per
month. Calculate his gross salary in
a month in which his sales
amounted to $40 000.00.
The gross wage for a salesman during a particular week is $646. If his basic wage is
$475 and he is paid a commission of 2.5% of the total value of the goods sold,
calculate;
(i) the commission that he was paid
(ii) the total value of the goods sold that week.
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CONSUMER ARITHMETIC
Income Tax
An income tax is a tax imposed on individuals or entities based on the income they
earned.
If an individual makes an amount that is less than or equal to a minimum amount,
then he does not have to pay income tax. If, however, an individual earns an income
which is greater than the minimum amount then he must pay income tax.
The total amount of money a person earns before tax is called the gross income.
Each individual has a number of allowances.
An allowance is part of the gross income that is non-taxable.
Once the income earner has deducted all legal allowances, the remaining amount is
the taxable income and is taxed depending on the rate.
Income Tax Allowances
•
Personal Allowance – an allowance for the income earner
•
Spouse Allowance – an allowance for the husband/wife who is not working
•
Child Allowance – an allowance for the children who are at school or university
•
Dependent Relative Allowance – an allowance for relatives dependent on the
taxpayer
•
National Insurance Allowance – an allowance for the national insurance
payments made
•
Insurance Premium Allowance – allowance paid on annuity policies
•
Credit Union Shares Allowance – an allowance for the purchase of credit union
shares
After the income earner has deducted all his legal allowances, the remaining amount
is called the taxable income.
This taxable income is then taxed at varying rates. The money remaining after paying
tax is called your net income.
𝑇ℎ𝑒 𝑡𝑎𝑥𝑎𝑏𝑙𝑒 𝑖𝑛𝑐𝑜𝑚𝑒 = 𝑇ℎ𝑒 𝑔𝑟𝑜𝑠𝑠 𝑖𝑛𝑐𝑜𝑚𝑒 − 𝐴𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒
𝑇ℎ𝑒 𝑛𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 = 𝑇ℎ𝑒 𝑔𝑟𝑜𝑠𝑠 𝑖𝑛𝑐𝑜𝑚𝑒 − 𝑇ℎ𝑒 𝑡𝑎𝑥 𝑝𝑎𝑖𝑑
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CONSUMER ARITHMETIC
E.g. 1 A teacher’s gross income is $42,500 per annum. He is married and his wife is not
employed. They have 2 children at school and 1 child at university. He pays $200/month
towards credit union shares and $900/month towards mortgage interest. The tax-free
allowances and his tax rates are as follows:
Calculate:
a)
His total tax-free income
b)
His taxable income
c)
The tax he pays per annum
Personal Allowance
$1500
Tax Rates
Spouse Allowance
$1000
Child (at school) Allowance
$200
5% on the first
$12,000
Child (at University)
Allowance
$500
15% on the
next $8000
Credit union shares
allowance
25% of total payment
35% on the
next $20,000
Mortgage interest
allowance
Total amount paid
National Insurance
Allowance
$30/month
40% on the
remaining
chargeable
income
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CONSUMER ARITHMETIC
1. Use the table below to answer the questions that follow
Single Person’s Allowance
$1500
Married Man’s Allowance
$2500
Child Under 11 Years Old
$400
Child Over 16 Pursuing Full Time
Education
$700
Dependent Relative
$250
National Insurance
$225
A married man with one child aged 17 attending university full time, and a second aged 9,
earns $25,600 per annum. He supports a dependent relative and also claims his national
insurance allowance.
Calculate:
a)
His total allowance
b)
His total total taxable income
c)
The amount he pays in tax per annum when it is levied at 40%
d)
The amount he pays in tax per month.
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CONSUMER ARITHMETIC
Profit and Loss
Cost Price = C.P. = the amount paid for the product
Selling Price = S.P. = the amount that the customer
pays for the article
𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑆𝑒𝑙𝑙𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒 − 𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒
= S.P. – C.P.
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑃𝑟𝑜𝑓𝑖𝑡 =
𝑃𝑟𝑜𝑓𝑖𝑡
× 100%
𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒
𝑆𝑒𝑙𝑙𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒 = 𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒 + 𝑃𝑟𝑜𝑓𝑖𝑡
𝐿𝑜𝑠𝑠 = 𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒 − 𝑆𝑒𝑙𝑙𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒
= C.P. – S.P.
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐿𝑜𝑠𝑠 =
𝐿𝑜𝑠𝑠
× 100%
𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒
𝑆𝑒𝑙𝑙𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒 = 𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒 − 𝐿𝑜𝑠𝑠
E.g. 1 A shopkeeper buys 25 cricket balls at a cost of $150.
a)
He sells them for $8 each, what is his profit?
b)
He sells them for $5 each, what is his loss?
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CONSUMER ARITHMETIC
1. A business woman bought a stove for
$1209.
a) Calculate the selling price of the
stove if she made a profit of 11%.
b) The stove was damaged in
transporting it to the customer.
Determine the selling price of the
stove if she incurred a loss of 8% on
the cost.
3.
2. A shopkeeper buys a stove from a
manufacturer for $860.
Calculate:
a) The selling price if he makes
a profit of 15%.
b) The selling price if he
incurred a loss of 15%.
A dealer buys 50 apples for $40 and sells them for $1.20 each. Calculate his
percentage profit
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CONSUMER ARITHMETIC
Percentage Change Examples
E.g. 1 A business woman sold a refrigerator for $2745 making a profit of 15% on the cost
price.
Calculate the cost price of the refrigerator to the businesswoman.
E.g. 2 A business man sold a refrigerator for $2149, incurring a loss of 12% on the cost price.
Determine the cost price of the refrigerator.
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CONSUMER ARITHMETIC
Percentage Change
1. A teacher’s salary was $3300 after
she had received an increase of 10%.
Calculate the teacher’s salary if she
had received an increase of 20%
instead.
3.
2. An entrepreneur sold a damaged
bedspread for $130.50 thereby
making a loss of 13% on the cost
price. Determine the cost price of the
bed spread.
When petrol was $2.40 per litre, I used 1200 litres per annum. The price increased by
150%, so I reduced my yearly consumption by 25%
Determine;
a. The new price per litre of petrol
b. The amount of my reduced annual consumption
c. The amount by which my petrol bill is more or less for the year.
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CONSUMER ARITHMETIC
Discount
This refers to a sale or an amount off the original price.
𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 = 𝑥% 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒
𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡𝑒𝑑 𝑃𝑟𝑖𝑐𝑒 = 𝑆𝑒𝑙𝑙𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒 − 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡
E.g. 1. A television set has a selling price of $1950. A 10% discount is offered for cash. What
amount is its cash price to the customer?
E.g. 2. In a sale, a cassette recorder was sold for $2071 after a discount of 5% was given.
Calculate the marked price of the cassette recorder.
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CONSUMER ARITHMETIC
1. A boutique is offering a 15% discount for cash. Calculate the cash price for a dress with
a marked price of $125.
2.
A salesman buys a stove from a manufacturer. The salesman sells the stove for
$1825.00 at a profit of 25%.
a. What amount did the salesman pay the manufacturer for the stove?
b. If the salesman gives 5% for cash, what amount does a customer pay for the stove?
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CONSUMER ARITHMETIC
Value Added Tax (VAT)
Value Added Tax is a tax paid buy the customer to the supplier for the Government,
this ranges from 10%- 20% generally. In Trinidad and Tobago it was recently
decreased from 15% to 12.5%. This is added to all goods and services.
Prices should be indicated before V.A.T and after V.A.T is included.
E.g. 1. The price of a lawnmower inclusive of VAT is $1050. Calculate the price of the
lawnmower exclusive of VAT.
E.g. 2. A DVD game player is priced at $2800 plus VAT at 15%. How many dollars does the
game actually cost the customer?
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CONSUMER ARITHMETIC
1. An airline ticket to New York is priced at $1232.10 inclusive of 11% sales tax. What
amount would the airline ticket cost exclusive of tax?
2.
The custom’s duty on imported vehicles is 25% of the imported price.
a. Calculate the customs duty on a car which the imported price is $16,800.
b. Calculate the imported price of a truck for which the amount paid, inclusive of
custom’s duty, is $69.750.
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CONSUMER ARITHMETIC
Hire Purchase
When someone doesn’t have all the money to purchase something or they prefer to
pay for it in parts they can use hire purchase.
This involves paying a down payment usually and paying the remainder of the cost of
the item in installments with interest.
𝐻𝑖𝑟𝑒 𝑃𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑃𝑟𝑖𝑐𝑒 = 𝐷𝑜𝑤𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 + 𝐴𝑚𝑜𝑢𝑛𝑡 𝑃𝑎𝑦𝑎𝑏𝑙𝑒
𝐴𝑚𝑜𝑢𝑛𝑡 𝑃𝑎𝑦𝑎𝑏𝑙𝑒 = 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝐵𝑎𝑙𝑎𝑛𝑐𝑒 + 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐶ℎ𝑎𝑟𝑔𝑒𝑑
E.g. 1. The marked price of a television set is $6980. If the customer pays cash, then the
price is 12% below the marked price. If the set is on hire purchase, then the buyer pays a
down-payment of $682.20 and 24 instalments of $344.06 each.
Determine for the television;
a. The cash price
b. The hire purchase price
c. The difference between the hire purchase price and the marked price
d. The percent interest charged on the outstanding balance
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CONSUMER ARITHMETIC
1.
Malia purchased a couch with a cash price of $2980 under hire purchase terms. She
paid an initial down-payment of 20% of the cash price and interest which is
equivalent to 15% of the outstanding balance is charged.
The balance is paid in 18 equal monthly instalments. Calculate for the video recorder:
a. The hire purchase price
b. The amount of each monthly instalment
c. The difference between the hire purchase price and the cash price
2.
The marked price of a freezer is $3000.00. There is a discount of 15% for cash payment.
To obtain the freezer on hire purchase, a deposit of $595.00 and 18 monthly
instalments of $159.50 each are required.
Calculate;
a. The cash price
b. the total amount paid if bought on hire purchase
c. the percentage difference of the cash price and the hire purchase price as a
percentage of the marked price.
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CONSUMER ARITHMETIC
Utility Bills
All households use basic services provided by private companies or the Government
on a daily basis. These include electricity, water, cable and internet access. The
charges depend on their usage, and the consumer is charged at regular intervals.
Some companies charge a fixed fee for the service and a variable charge based on
consumption.
E.g. 1. A company charges the following monthly rate for all local telephone calls
First 15 calls or less
45 cents per call
Remaining calls
30 cents per call
Calculate the total bill for each of the following customers.
i.
Judy who made 12 local calls for the month.
ii.
Chris who made 52 local calls for the month.
E.g. 2. The information displayed is the table below is an extract from Mr. Sandy’s electricity
bill for a period of one month.
Meter Reading (kWh)
Previous
Present
5833
6925
Fuel Charge
Energy
Charge
VAT
25 cents per
kWh
20 cents per
kWh
15% of total
bill
Calculate;
i.
The number of units in kWh used by Mr. Sandy for the month.
ii.
Mr. Sandy’s bill, inclusive of VAT for the month.
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CONSUMER ARITHMETIC
1. Charges in a CARICOM for electricity are made up of a fixed fuel charge of 35 cents
per kWh and an energy charge computed under three schemes as follows.
Scheme A: Homes – 15 cents per kWh
Scheme B: Schools – 20 cents per kWh
Scheme C: Business Places– 25 cents per kWh
Meter Reading (kWh)
Present
Previous
72471
47523
kWh used
Scheme
Energy
Charged ($)
Fuel Charge ($)
B
Calculate:
a) The number of kilowatt-hour used.
b) The energy charge in dollars
c) The fuel charge in dollars
d) The amount the school had to pay for the electricity used.
e) The actual amount the school paid if a discount of 10% was given for cash
2. In January, Mr. Amin’s telephone bill was calculated on the following information
Long Distance Calls To
Duration of Calls in
Minutes
Fixed Charge for 3mins
or less
Charge per Additional
Minute
Ontario
25
$17.65
$5.90
New York
37
$15.40
$5.35
Paris
19
$19.20
$6.50
Monthly rental for telephone = $25.50
Calculate Mr. Amin’s actual telephone bill for January.
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CONSUMER ARITHMETIC
Simple Interest
Money may be borrowed or invested by individuals or financial institutions for any
purpose. Some payment, called interest, has to be made for the use of that money.
The sum of money borrowed or invested is called the principal. The amount earned is
the sum of the principal and the interest earned or acquired when there was an
investment or due when there was a loan.
If $P was invested or borrowed for a period of T years at a rate of R% per annum, the
simple interest, I is calculated by;
𝐼=
𝑃𝑅𝑇
100
E.g. 1. Josiah agrees to take a loan from a bank and repay at the rate of 12% simple interest
per annum for 3 years. His total interest is calculated to be $5400. How much money is
Josiah borrowing?
1. A flat screen TV costs $5800. Ulric, is offered the set with no money down and 10% simple
interest over a 3year period.
i.
How much interest will Ulric pay?
ii.
What is the total amount for the TV?
iii.
What is the equal monthly installments?
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CONSUMER ARITHMETIC
Compound Interest
If the interest earned or paid on investments is added to the principal at given
intervals, then the interest is said to be compounded over the time period. This type of
interest is called Compound Interest. The interest earned over a period is added to
the principal to form a new principal. The next period the interest is earned on the
new principal. Consequently, the principal increases periodically throughout the term
of the transaction and therefore so does the interest.
When the principal is invested at a rate of R% over a period of n years. The total
amount is found using;
𝑇𝑜𝑡𝑎𝑙 = 𝑃( 1 +
𝑅 !
)
100
E.g. 1. Calculate the compound interest on $6000 if invested for a period of 3years at 7 ½%
per annum.
1. Find the amount accrued on the sum of $7263.50 at the rate of 5 ¼ % compound
interest per annum over a period of 3 ½ years.
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CONSUMER ARITHMETIC
Appreciation and Depreciation
Just as interest is compounded on investments and loans, the same can be said for
some valuables and property. It is useful to note that the principle used in calculating
compound interest is the same as the principle used in calculating appreciation and
depreciation.
Appreciation is an increase in the value of an asset over time.
𝑅 !
𝑇𝑜𝑡𝑎𝑙 = 𝑃( 1 +
)
100
Depreciation is a decrease in the value of an asset over time.
𝑅 !
𝑇𝑜𝑡𝑎𝑙 = 𝑃( 1 −
)
100
E.g. 1. An item of jewelry originally valued at $1000 appreciates by 10% each year. What is
the expected value after 2 years?
1. A car valued at $20,000 depreciates by 10% each year. What is the expected value
after 3 years?
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CONSUMER ARITHMETIC
Foreign Exchange
1. Given that US$1.00 is equivalent to
TT$6.24.
Calculate the amount in US Currency
that is equivalent to TT$936
3.
2.
Given that
TT$1.00 = EC $0.43
TT$6.30 = US$1.00
Convert;
a) TT$125.00 TO EC$
b) EC$850.94 TO US$
In July 2004, a Canadian tourist changed CAN$1500 of her Canadian travellers’
cheques for Trinidad and Tobago currency. One third of this amount was in $50
cheques and the remainder was in $100 cheques.
CAN$1.00 = TT$4.70
13 cents on the dollar is charged for tax on the total foreign exchange transaction.
TT$0.30 stamp duty is charged per cheque.
@Royanne’s Study Corner