# COMMERCIAL ARITHMETIC

**FIRST TERM **

**LEARNING NOTES**

**CLASS: JSS 2 (BASIC 8)**

**SCHEME OF WORK WITH LESSON NOTES **

**Subject: **

### MATHEMATICS

**Term:**

**FIRST TERM **

**Week:**

**WEEK 7**

**Class:**

**JSS 2 (BASIC 8)**

**Previous lesson: **

The pupils have previous knowledge of

** TRANSACTIONS IN THE HOMES AND OFFICES**

that was taught as a topic during the last lesson.

**Topic :**

# COMMERCIAL ARITHMETIC

**Behavioural objectives:**

At the end of the lesson, the pupils should be able to

- solve simple mental sums on commercial mathematics
- solve questions on Commercial Arithmetic (simple interest, profit and loss, discount, commission, VAT, hire purchase)
- Exchange rate

**Instructional Materials:**

- Wall charts
- Pictures
- Related Online Video
- Flash Cards

**Methods of Teaching:**

- Class Discussion
- Group Discussion
- Asking Questions
- Explanation
- Role Modelling
- Role Delegation

**Reference Materials:**

- Scheme of Work
- Online Information
- Textbooks
- Workbooks
- 9 Year Basic Education Curriculum
- Workbooks

**Content**

**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 as a 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

N20000 + 5% of N20000 = N20000 + N1000

= N21000

The interest is N1000 and the amount you now have in your saving account is N21000

**Note that (Amount = principal + interest).**

**Example 2:**

Mr. Alabi saves N50000 with a bank for 1 year with interest at 5 ½ % per annum.

(a) Calculate the interest he will receive at the end of the year.

(b) Calculate the simple interest for 4 ½ years.

(c) What is the total amount he will save at the end of 4 ½ years

Solution:

(a) Interest = 5 ½% of ₦50000

= [Math Processing Error]

= 0.055 × 50000 = ₦2750

(b) Interest for 1 year = ₦2750

Interest for 4 ½ years = ₦2750 × 4 ½

= ₦2750 × 4.5

Simple interest = ₦12 375

Amount saved = principal + interest = ₦50000 + ₦12 375 = ₦62 375

**Class Activity**

**Find the simple interest of the following:**

(i) 10000 for 1 year at 4% per annum

(ii) 15000 for 2years at 6% per annum

(iii) 20000 for 1year at 4 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**

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

**Solution:**

Profit = 15% of ₦800 = [Math Processing Error]

Selling price = ₦800 + ₦120

= ₦920

(ii) A hat is bought for ₦250 and sold for ₦220. What is the loss per cent?

**Solution**

Actual loss = ₦250 − ₦N220 = ₦30

The ratio, loss: cost = ₦30: ₦250 = 30: 250

= [Math Processing Error]

Thus the loss is [Math Processing Error] of the cost price.

Percentage loss = [Math Processing Error] = 12%

**Class Activity**

- A farmer buys a cow for ₦40000 and sells it for ₦33000 What is the percentage loss?
- A trader bought some compact disc for ₦350 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 ₦140 each or four for ₦440. How much is saved by buying four packets at once instead of separately?

**Solution**

1 packet of tissues = ₦140

4 packets = 4 × ₦140 = ₦560

Discount price of 4 packets = ₦440

Savings = ₦560 − ₦440

= ₦120

(ii) A radio costs ₦5400. A 12 ½ % discount is given for cash. What is the cash price?

**Solution**

Method 1:

Discount = 12 ½ % of ₦5400

Cash price = ₦5400 − ₦675

= ₦4725

Method 2:

Cash price = [Math Processing Error] of ₦5400

**Class Activity**

- The selling price of a chair is ₦14000. The trader gives a 25% discount for cash. What is the cash price?
- Find the discount price if a discount price of:

(a) 10% is given on a cost price of ₦430

(b) 12 ½ % is given on a cost price of ₦280

**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 ₦10 500 each and nine small fans at ₦5400 each. Calculate his commission.

Total sales = 4 x ₦10500 + 9 x ₦5400

= ₦42 000 + ₦48 600

= ₦90600

He gets 14k for every naira.

Commission = 90600 x 14k

= 1268400k

= ₦12684

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

= 2 ½% of ₦84000

= 2 ½ x [Math Processing Error] × ₦84000

= [Math Processing Error] × ₦84000

= ₦2100

Total cost of Bank Draft = value of Bank Draft + commission

= ₦84000 + ₦2100

= ₦86100

**Class Activity**

- A rent collector’s commission is 4 ½ of his takings. In one month he collects ₦842800 in rent. How much money does he get?
- 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:**

(i) An advertisement for a table says that its price is ₦15 300 plus 5% VAT. How much does the customer pay?

**Solution**

Amount paid by customer = 105% of ₦15300

= ₦15300 X [Math Processing Error]

= ₦16065

**Note: **The difference between ₦16065 and ₦15300 is ₦765. The Government receives ₦765 as Vat

- One year a company paid a ₦94500 telephone bill to NITEL. The bill included VAT at 5%. Calculate how much money the Government receives as VAT on the bill.

**Solution**

Since ₦94500 includes 5% VAT, then ₦94500 is 105% of the actual telephone bill. The VAT is 5% of the actual telephone bill.

1% of actual bill = [Math Processing Error]

= ₦900

5% of actual bill = ₦900 × 5

= ₦4500

The government receives ₦4500 as VAT

** **

**Class Activity**

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

COMFORT FURNISHING

Small tables | ₦5670 | |

Mattresses | ₦9240 | |

Beds | ₦21630 | |

3-piece suites | ₦31290 | |

Kitchen tables | ₦6930 | |

**Hire Purchase**

An **installment** is a part payment. Many people find it easier to buy expensive items by paying installments.

Buying by installment 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 ₦2750. Find the difference between the installment price and the cash price.

**Solution **

**Installment price = deposit + installment**

= ₦4000 + 12 × ₦2750

= ₦4 000 + ₦33 000

= ₦37 000

Price difference = ₦37 000 − ₦34 000

= ₦3 000

**Class Activity **

The hire purchase price of a computer is ₦84000. 25% is paid as a deposit. The rest is spread over 12 equal monthly installments.

(a) Calculate the amount of the deposit.

(b) Calculate the remainder to be paid.

(c) Find the amount of each monthly installments

** **

**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.

(a) How much does the woman pay?

(b) 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?

**Presentation**

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

### Evaluation

- A market trader asks #5000 for some cloth. A woman offers #1 200. After bargaining, they agree a price half-way between the two starting prices.
(a) How much does the woman pay?

(b) What discount did she get by bargaining?

- The cash price of a used car is #500,000. To pay by hire requires a 10% deposit and 36 monthly payments of #24 420. Calculate the total amount of money that will be paid back by the hirer
- A bicycle can be bought either in cash for #247000 or by paying 52 weekly payments of #5400.Which amount is the higher price
- A history book costs #850. The writers of the book get 10% of the price of each book 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?
- What is the simple interest on #120, 000 at the rate of 5% per annum for 12 years?
- The price of a car is #2 500 000. If 15% VAT is payable on the purchase. How much does a prospective buyer pay?
- An estate agent got 15% as commission on rental of #450 000. How much did he get?
- A customer deposits a cheque for #500 000. Her bank charges 12% 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?

**Conclusion**

The class teacher wraps up or concludes the lesson by giving out a short note to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she makes the necessary corrections when and where the needs arise.

** **