## Commercial Arithmetic Photo: Commercial arithmetic

Commercial Arithmetic

Commercial arithmetic is a branch of mathematics that deals with money matters. Commercial arithmetic is used in many areas of our daily activities. Under commercial arithmetic’s we have the simple interest, compound interest, appreciation and depreciation, hire purchase and taxes.

Simple interest

Interest is the price for the use of borrowed money for a specific period of time. If a sum of money is deposited in or borrowed from a financial institution for a period of time, it earns interest. The sum of money deposited or borrowed is called principle (P). The ratio of interest earned in a given period of time to the principle is called rate (R) of interest. The rate of interest is usually expressed as a percentage per annum of the principal. Per annum (p.a.) means yearly.

When interest is calculated using only the initial principal at a given rate and time it is called simple interest (I)

Example 1

What is the simple interest earned on sh. P at a rate of R% per annum for T years?

Solution

Simple interest (I)=Principal (P) *Rate (R) * Time (T) /100

Abbreviated as I=PRT/100 this is the simple interest formula

Example 2

What is the simple interest earned on \$ 2,000 at 12% per annum for (a) 1-year (b) 2years (c) 3 years?

Solution

Interest earned is:

(a)    \$12/100*2000*1=\$240

(b)    \$ 12/100*2000*2=\$480

(c)     \$ 12/100*2000*3=\$720

Compound interest

If money is borrowed from or deposited in a financial institution It earns interest after a specified period of time at the stated rate of interest. Instead of interest being paid out to the owner, it may be added to (compounded with) the principle and thereafter also earn interest.

Example

Find the amount after 2 years if \$1,000 is invested at 15% p.a. compound interest

Solution

1st year interest=\$.15/100*1000=\$sh150

Amount after 1st year. =\$. (1000+150) = \$1150

2nd year interest =\$ 15/100*1150 = \$. 172.50

Amount after 2nd yr. =\$. (1150+172.50)

=\$.1322.50

Explanations such interest which is added to the principal is called compound interest. The period after which it is compounded to the principal is referred to as the interest period. The compound interest may be calculated annually, semi-annually, quarterly, monthly, etc.

After every interest period the principal increase and therefore the interest earned also increases. The sum of the principal and the compound interest is called the accumulated amount.

Appreciation and depreciation

Machines and building experience wear and tear with time. Because of this they lose their value. The loss in value of an asset with time is called depreciation if however, an asset gains in value with time it is said to have appreciated. For example, the value of land in urban centers keeps on increasing due to high demand.

Example an iron box costs \$.500 and depreciates each year by 10% of its value at the beginning of the year. What will be its value after 4 years?

Solution

Value after the first year =\$. (500-500*10/100)

=\$.450

Value after the second year= \$. (450-450*10/100)

= \$. 405

Value after the third year = \$. (405-405*10/100)

= \$. 364.50

Value after the fourth year = \$. 364.50-364.50 *10/100)

= \$. 328.05

Show that the value of the iron box after 4 years is

=500(1-10/100)^n

Hire Purchase

Frequently, many individuals find themselves compelled to make huge cash outlays for worthwhile purchase or for emergencies. Most often, they do not have the necessary cash and have to either borrow the money or buy on credit. To buy on credit means to make a down payment and then pay the balance by instalment (usually regular).

In this method interest has to be paid on borrowed money. The rate of interest charged depends on the time, the amount and the lending body.

Example

Peris wants to buy a sewing machine on hire purchase. It is marked \$. 7,500 cash. She can pay the price or make a down payment of \$2,250 and 15 monthly instalments of \$ 550 each

How much interest does she pay under the instalment plan?

Solution

Total amount of instalments = \$. 550*15 = \$.8,250

Down payment                                                 =\$.2,250

Total                                                                      = \$.10,500

Amount of interest = \$. (10,500-7,500) =\$. 3,000

Note Peris will be able to take the sewing machine as soon as she pays the down payment.

The interest charged for buying goods/services on credit is called a carrying charge which is calculated as a compound interest. Such a method of buying items by instalment is called HIRE PURCHASE

Taxes

To provide services such as health, education, roads, etc. the government has to raise funds. One of the main sources of revenue for the government is through taxation. Tax is charge levied on individuals and companies for the purpose of providing government services. There are two main types of taxes: direct and indirect taxes

Direct taxes include income tax (levied on the income of individuals) corporate tax (levied on profits of companies), capital gain tax (levied on properties), VAT and estate duties (levied when a person who has property dies)

Indirect taxes include sales tax (levied on some consumer goods and services) excise duties (levied on goods manufactured locally), Custom duties (levied on goods imported from outside the country) and export duties (levied on goods exported from the country

Example

If a 110% duty is charged on a bottle of beer, which costs \$ 4.50 to produce, calculate the selling price

Solution

Duty =\$. 110/100*\$. 4.94

Selling price =\$. (4.95+ 4.50) = \$. 9.45