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Commercial Arithmetic II - Mathematics Form 3


Credit traders allow customers to buy such items like T.V, Fridges,sewing machines, etc so that they acquire them on credit, since they involve huge sums of money.

To buy the item, the creditor allows the customer to pay a deposit and make payments of the balance byinstalments with an Interest.

Government Revenue is collected by income tax department and deposited at the Central Bank. This money is budgeted for and disbursed by the treasury to facilitate development in various areas in the country.


The following are hire Purchase Shops (AMEDO, KCT, ART etc).

Some of the items likely to found in a hire purchase shop are

T.V s, Refrigerators, Sewing,Machines, Motorcycles.


Income Tax is deduction on money made from employment, business or capital. It is charged on money earned by individuals, organisations from employment, or business entities or capital.Tax which is paid to the government from salaried persons, is known as Income Tax. This tax is deducted by employers from their employees' salaries monthly through a system known as Pay As You Earn (P.A.Y.E ).

In order to calculate P.A.Y.E , a table giving Tax Bands which are provided by the government is used.

Example 2

Mary pays a tax of Kshs 2,272 per month after a tax relief of Kshs 1,056.Calculate her salary.

Step 1
Add the Relief to PAYE
Kshs ( 1,056 + 2,272 ) = Kshs 3,328 which is the total tax before being relieved.

Step 2
Consider the Income Tax Bands in example 1.
The First Band
9,680------------------------- 10/100 x 9,680 = Kshs 968
The Second Band
9,120------------------------ 15/100 x 9,120 = Kshs 1,368
If you continue in the next band, we find that, the sum exceeds Kshs 3,328 which we need. We therefore get the difference { 3,328 - ( 968 +1,368) } = Kshs 992

Step 3
We consider the Tax rate in the next Band and assume the amount to be taxed is kshs. Y.

Step 4
Consider the lower limit of the 3rd band 18,801 - 27, 920 i.e. 18, 800 then add it to 4,960 to get her monthly salary. Kshs (4,960 + 18, 800) = kshs 23, 760 per month. An employee is entitled to certain benefits (allowances) such as house allowance, medical allowance, and commuter allowance, etc. during PAYE calculation; allowances are added to the basic salary to form Taxable income. Any time an employee is taxed, they must be given tax relief, referred to as 'Personal Relief', which in this example is kshs 1,056.

Example 3
John earns a basic salary of Kshs 33,600. He also receives a house allowance of Kshs 20,000 per month and a medical allowance of Kshs 3,200 per month.
Calculate the amount of Income Tax he pays

Taxable Income is obtained by adding the basic salary and the allowances ie
Basic salary Kshs 33,600
House allowance Kshs 20,000 +
Medical allowance Kshs 3,200
TOTAL Kshs 56,800

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