Commercial arithmetic

Simple Interest

If you save your money with a bank, you will be paid some extra money called interest. On the other hand, if you borrow money from a bank you pay interest to the bank. The original money invested or borrowed is known as the principal or capital. The interest rate is often given in percentage and quoted as a rate per annum. For example, 5% rate means that the interest paid or received every year is 5% of the principal.

Example 1:

If you save N20000, then at the end of the year you will have your original money (principal) plus the interest

N20 000 + 5% of N20 000 = N20 000 + N1000

= N21 000

The interest is N1000 and the amount you now have in your saving account is N21 000

Note that (Amount = principal + interest).

Example 2:

Mr. Ogbeha saves N50 000 with a bank for 1 year with interest at 5 ½ % per annum.

1. Calculate the interest he will receive at the end of the year.
2. Calculate the simple interest for 4 ½ years.
3. What is the total amount he will save at the end of 4 ½ years

Class Activity

            Find the simple interest of the following:

1. 10000 for 1 year at 4% per annum
2. 15000 for 2years at 6% per annum
3. 20000 for 1year at 4 1 ½ per annum

Profit and loss

         The cost at which a trader obtains his goods is called Cost Price (C.P). the price at which the trader sells the goods is called the selling price (S.P).

When the selling price is greater than the cost price, a profit is said to be made and

Profit = selling price – cost price

If the selling price is less than the cost price, a loss is said to be made and

Loss = cost price – selling price

Sometimes, the word gain is used in place of profit.

Example

• A trader buys a kettle for and sells it at a profit of 15%. Find his actual profit and the selling price.

Class Activity

1. A farmer buys a cow for N40000 and sells it for N33 000. What is the percentage loss?
2. A trader bought some compact disc for N350 each. She sold them at a 12% profit. What was the selling price?

Discount

      A discount is a reduction in price. Discounts are often given for paying in cash.

Example

• A trader sells packets of tissues at N140 each or four for N How much is saved by buying four packets at once instead of separately?

Solution

I packet of tissues       = N140

4 packets = 4 X N140             = N560

Discount price of 4 packets    = N440

Savings                                    = N560 – N440

= N120

• A radio costs N A 12 ½ % discount is given for cash. What is the cash price?

Solution

Method 1:

Class Activity

1. The selling price of a chair is N The trader gives a 25% discount for cash. What is the cash price?
2. Find the discount price if a discount price of:
3. 10% is given on a cost price of N430
4. 12 ½ % is given on a cost price of N280

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. Likewise 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 N10 500 each and nine small fans at N5400 each. Calculate his commission.

Total sales = 4 x N10 500 + 9 x N5400

= N42 000 + N48 600

= N90 600

He gets 14k for every naira.

Commission = 90600 x 14k

= 1 268 400k

= N12 684

• A bank charges 2 ½ % commissions for issuing a Bank Draft to its customers. If a customer obtained a Bank draft for 84000 from the bank, calculate the total cost of the Bank Draft.

Solution

Commission paid to the bank

Class Activity

1. A rent collector’s commission is 4 ½ of his takings. In one month he collects 842 800 in rent. How much money does he get?
2. A car salesman gets 1k in the naira commission. Calculate his commission if he sells 5 238 000 worth of cars in a month.

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), the goods and services are called VATable items.

Example:

• An advertisement for a table says that its price is N15 300 plus 5% VAT. how much does the customer pay?

Note: The difference between N16 065 and N15 300 is N765. The Government receives N765 as Vat

• One year a company paid a N94500 telephone bill to NITEL. The bill included VAT at 5%. Calculate how much money the Government receives as VAT on the bill.

Solution

Since N94500 includes 5% VAT, then N94500 is 105% of the actual telephone bill. The VAT is 5% of the actual telephone bill.

Class Activity

Find the amount of money that the Government        receives as VAT on each item in the following advertisement:

Hire purchase

An instalment is a part payment. Many people find it easier to buy expensive items by paying instalments.

Buying by instalment is called hire purchase. The buyer hires the use of an item before paying for it completely. This is why hire purchase is more costly than paying in cash.

Example

The cost of a DVD player is either #34 000 in cash or deposit of #4 000 and 12 monthly payments of N2750. Find the difference between the instalment price and the cash price.

Solution

Instalment price = deposit + instalment

= N4000 + 12 x N2750

= N4 000 + N33 000

= N37 000

Price difference           = #37 000 – N34 000= N3 000

Class Activity

The hire purchase price of a computer is N84000. 25% is paid as a deposit. The rest is spread over 12 equal monthly instalments.

1. Calculate the amount of the deposit.
2. Calculate the remainder to be paid.

Find the amount of each monthly instalments

PRACTICE QUESTIONS

• What is the simple interest on #12, 000 at the rate of 3% per annum for 6 years?
• The price of a car is #2 500 000. If 5% VAT is payable on the purchase. How much does a prospective buyer pay?
• An estate agent got 12% as commission on rental of #450 000. How much did he get?
• A customer deposits a cheque for #50 000. Her bank charges 2% commission for clearing the cheque. Calculate how much money is credited to her account.
• By selling goods for #5 350 a trader makes a profit of 7%. She reduces her prices to #5 150. What is her percentage profit now?
• A television set costs either #49 400 cash or weekly payments of #1 145. How much more does the television set cost when paid for weekly?

ASSIGNMENT

• A market trader asks #2500 for some cloth. A woman offers #1 200. After bargaining, they agree a price half-way between the two starting prices.

1. How much does the woman pay?
2. What discount did she get by bargaining?

• The cash price of a used car is #897 060. To pay by hire purchase requires a 10% deposit and 36 monthly payments of #24 420
• A bicycle can be bought either in cash for #24 700 or by paying 52 weekly payments of #540.
• A history book costs #850. The writers of the book get 10% of the price of each books sold. How much will they get if it sells 15 628 copies in one year?
• A villager bought 11 goats for #76 000. A year later he sold them at a profit of 32%. What was the average selling price per goat?