JSS 2 Mathematics Second Term Week 2
Topic: ARITHMETIC IN THE HOME AND OFFICE
Personal Arithmetic
Interest
Bankers want people to save money. They give extra payments to encourage saving. The extra money is called interest.
For example, a person saves N10 000 in a bank for a year. If the interest rate is 8% per annum (i.e. 8% per year), the saver will have N10 800 at the end of the year: the original N10 000 plus N800 interest from the bank. Interest that is paid like this is called simple interest.
Example
Find the simple interest on N60 000 for 5 years at 9% per annum.
Yearly interest = 9% of N60 000
= 9/100 X N60 000 = N5 400
Interest for 5 years = N5 400 X 5 = N27 000
Exercise
Find the interest on the following:
1. N40 000 for 1 year at 5% per annum
2. N70 000 for 1 year at 4% per annum
3. N10 000 for 3 years at 6% per annum
4. N10 000 for 2 years at 4% per annum
5. N10 000 for 4 years at 4½ per annum
Sometimes people borrow money. When someone borrows money that person has to pay interest to the lender.
Example
A man borrows N1 600 000 to buy a house. He is charged interest at a rate of 11% per annum. In the first year he paid the interest on the loan. He also paid back N100 000 of the money he borrowed. How much did he pay back altogether? If he paid this amount by monthly installments, how much did he pay per month?
Interest on N1 600 000 for 1 year
= 11% of N1 600 000
= 11/100 X N1 600 000
= 11 X N16 000
=N176 000
Total money paid in 1st year
=N176 000 + N100 000
= N276 000
Monthly payments = N278 000 ÷ 12
= N23 000
(Notice that the man now owes N1 500 000. Interest will be paid on this new amount in the second year.)
Exercise
Find the total amount to be paid back (i.e. loan + interest) on the following loans:
a. N500 for 2 weeks at N100 interest per week.
b. N2 000 for 3 weeks at N1 on each N10 interest per week
c. N1 000 for one year at 9% simple interest per annum.
INCOME TAX
Most people have to pay part of their income to the government. The part they pay is called income tax. This process is often called PAY E (Pay As You Earn). The government uses taxes to pay for public services such as defence, education, health and transport.
The method of calculating taxes varies in different countries and tax rates change from time to time. However, the method is usually similar to the following example.
Typical PAY E tax system
1. Each month, all earners pay tax on their taxable income. Table below contains typical rates of tax, for various income bands.
| Tax bands on monthly income | Rate of tax |
| First N20 000 | 10% |
| Over N20 000 and up to N40 000 | 15% |
| Over N40 000 and up to N60 000 | 20% |
| Over N60 000 | 25% |
2. For any wage or salary earner, taxable income = total income – allowances.
3. Allowances are as follows:
a. personal allowance: N6 000
b. child allowance: N2 500 for each child under 16 t-years of age (for am maximum of 4 children)
c. dependent relative allowance: maximum of N4 000.
If both husband and wife are working, the child allowance can only be claimed by one parent
Example
A man has a total income of N52 800 per month. He has 3 young children. He claims N3 700 for a dependent relative. Calculate the amount of tax he pays.
First: calculate the allowances.
Personal allowance = N6 000
Child allowance = 3 X N2 500 = N7 500
Dependent relative = N3 700
Total allowances = N17 200
Second: calculate the taxable income.
Taxable income = total income – allowances
= N52 800 – N17 200
= N35 600
Third: Calculate the tax on the taxable income, using the tax band table sighted above, using it.
Taxable income = N35 600 – N20 000 + N15 600
Tax = 10% of N20 000 + 15% of N15 600
= N2 000 + N2 340
= N4 340
Notice the following:
1. Everyone gets the personal allowance of N6 000. Thus anyone earning N6 000 a month or less will pay no tax.
2. Always work in the following order:
First – find the allowances,
Second – calculate the taxable income,
Third – calculate the tax.
Exercise
A person with 5 children earns N61 320 per month.
a. Calculate the tax allowances.
b. Calculate the taxable income
c. Calculate the amount of tax paid
d. Calculate the income after tax is paid.
Household Arithmetic
DISCOUNT BUYING
A discount is a reduction in price. Discounts are often given for paying in cash.
Example
A radio costs N5 400. A 12½% discount is given for cash. What is the cash price?
Either,
Discount = 12½% of N5 400
= 12½/100 X N5 400
= N675
Cash price = N5 400 – N675 = N4 725
or,
cash price = (100% – 12½ %) of N5 400
= 87½ % of N5 400
= 87½ /100 X N5 400
= 7/8 X N5 400
= N4 725
Discounts are often given buying in bulk.
INSTALLMENT BUYING
An installment is a part of payment. Many people find it easier to buy expensive items by paying installments.
Example
The cost of a DVD player is either N34 000 in cash or deposit of N4 000 and 12 monthly payments of N2 750. Find the difference between the installment price and the cash price.
Installment price = deposit + installment
= N4 000 + 12 X N2 750
= N4 000 + N33 000
= 37 000
Price difference = N37 000 – N34 000
= N 3 000
Buying by installment is called hire purchase. The buyer hires the bus of an item before paying for it completely. This is why hire purchase is more costly than paying in cash.
CIVIC ARITHMETIC
Value Added Tax (VAT)
A proportion of the money paid for certain goods and services is given to the government. The part which is given to the government is called Value Added tax (VAT), and the goods and services are called VATable items.
In Nigeria 5% of the cost of VATable items is given to the government as VAT. The government uses money collected as VAT to improve services such as education, health and transport.
Example
An advertisement for a table says that its price is ‘N15 300 plus VAT’. How much does the customer pay?
Amount paid by customer = 105% of N15 300
= N15 300 X 105/100
= N16 065
Note: The difference between N16 065 and N15 300 is N765. The Government receives N765 as VAT.
BILLS AND CHARGES
Electricity bills
Electricity bills are based on the number of units of electricity used. Also there is usually a standing charge, or Demand charge, and VAT is charged. The table below gives typical charges.
| Cost per unit | N8 |
| Standing charge | N150 per quarter |
| VAT | 5% of total bill |
Example
A company’s electricity meter reading changed from 45 243 to 50 548 in one quarter. Use the table above to calculate the company’s electricity bill.
Number of units used = 50 584 – 45 243
= 5 341
Cost at N8 per unit = N8 X 5 341
= N42 728
Standing charge = N150
Total charges = N42 728 + N150
= N42 878
Total bill, including VAT = N42 878 X 105%
= N42 878 X 105/100
= N45 021.90 (calculator)
= N45 022 to nearest naira
Postal charges
Postal charges vary according to the weight of the letters and parcels being posted by and their destination. The table below gives some typical charges.
| Letters up to 20 g | |
| Letters within a state | N20 |
| Letter between states | N50 |
| Letters outside Nigeria | N100 |
| Parcel within Nigeria | |
| ≤ 1kg | N200 |
| > 1kg and ≤ 2kg | N400 |
COMMERCIAL TRANSACTION
Profit and loss
A trader buys a kettle for N800 and sells it at a profit of 15%. Find his actual profit and the selling price.
Profit = 15% of N800 = 15/100 X N800
= N 12 000/100
= N120
Selling price = N800 + N120
= N920
Example
A hat is bought for N250 and sold for N220.
What is the loss percent?
Actual loss = N250 – N220
= N30
The ratio, loss : cost = N30:N250
= 30 : 250
= 30/250
Thus the loss is 30/250 of the cost price
Percentage loss = 30/250 X 100%
= 12%
Notice that the loss or gain is calculated as a percentage of the cost price.
COMMISSION
Commission is payment for selling an item. For example, insurance agents get commission for selling insurance. The more insurance they sell the more commission they get. Factories often employ sales representatives to sell their goods to shops and traders. The sales representatives often receive a proportion of the value of the goods they sell. This proportion is their commission.
Example
A sales representative works for an electric fan company. he gets a commission of 14k in the naira. In one week he sells four table fans at N5 400 each. Calculate his commission.
Total sales = 4 X N10 500 + 9 X N5 400
=N42 000 + N48 600
= N90 600
He gets 14k for every naira.
Commission = 90 600 X 14k
= 1 268 400k
= N12 684
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