Commercial Maths : Money Simple Interest, Discount and Commission, Money Transaction
SUBJECT: MATHEMATICS
CLASS: BASIC FIVE / PRIMARY 5
TERM : SECOND TERM
WEEK : WEEK 6
TOPIC : COMMERCIAL MATHEMATICS : MONEY
- Simple Interest
- Discount and Commission
- Money Transaction
Importance
- Discount on sales draw draw customers to sales and services
- Money most importantly functions as a medium of exchange to facilitate transaction
- Money is used to settle bills for family needs eg education, health, care, charity, vacation, trips etc
Learning Objectives :
Pupils should be able to
- Explain simple interest in business transactions
- Solve problems on discount and commission
- Calculate discount, commission, simple interest in real life problems eg post office, market, etc
- Solve problems involving money transaction
- Understand and calculate simple interest.
- Understand and calculate discounts.
- Understand and calculate commission.
Learning Activities :
- Pupils as a class do a role play of class business. Pupils are shared into two groups. A group sells products while another group buys products.
- Charts on money are placed all around the class and dummy money are given to the pupils
- Pupils in class as groups brainstorm on giving different ways a smaller denomination can make up a bigger denomination and breaking down the bigger denomination to smaller denomination
- Pupils in small groups use dummy money or photocopy money to work on the conversion the Nigeria currency ( Naira is converted to other country currency and vice versa)
- Pupils do a role play on obtaining discount on sales of items and also on getting commission from a company on a sales of products
Embedded Core Skills
- Critical thinking and problem solving skills
- Communication and Collaboration
- Student Leadership skills and Personal Development
Learning Resources
- Paper or dummy money
- Recording sheet
- Calculator
- Whiteboard and markers
- Textbooks and Workbook with simple interest, discount, and commission formulas and examples
Content
Simple interest is the additional amount of money that is made by an initial deposit in a bank. The old initial deposit is referred to as principal. Any money that is deposited in the bank is applied to a rate that is always determined or fixed by the bank. The rate is always in percentage.
When the initial amount of money is saved in the bank for a period of time, then simple interest is made.
Simple interest is a method of calculating the interest charge on a loan or deposit, typically involving a fixed interest rate and a fixed period of time. The formula for simple interest is: I = Prt, where I = interest P = principal (the initial amount of the loan or deposit) r = annual interest rate (expressed as a decimal) t = time (in years)
Worked Examples
- If a person takes out a loan of NGN 50,000 at an interest rate of 5% per year for 2 years, how much interest will they pay? I = Prt I = (50000)(0.05)(2) I = NGN 5,000
- If a person deposits NGN 100,000 into a savings account with an annual interest rate of 3% for 4 years, how much interest will they earn? I = Prt I = (100000)(0.03)(4) I = NGN 12,000
- If a person takes out a loan of NGN 150,000 at an interest rate of 6% per year for 3 years, how much will they have to pay back in total? Total = P + I Total = (150000) + (150000)(0.06)(3) Total = NGN 195,000
- If a person has a credit card balance of NGN 20,000 with an annual interest rate of 15%, how much interest will they pay in 1 year? I = Prt I = (20000)(0.15)(1) I = NGN 3,000
- If a person wants to save NGN 500,000 in a savings account with an annual interest rate of 2%, how many years will it take to reach their goal if they make no additional deposits? P = I / rt t = I / Pr t = (500000) / (0.02)(100000) t = 25 It will take 25 years
How to calculate principal when interest, rate or time is already known
- Olusegun has taken a loan of ₦100,000 with an interest rate of 6% per year for 2 years. The total amount he has to pay back is ₦112,000. To calculate the principal, we can use the formula: P = Total – I P = 112000 – (0.06)(2)(100000) P = 100,000
- Oludare deposited ₦120,000 in a savings account for 3 years at an interest rate of 5%. The total amount he has after 3 years is ₦138,800. To calculate the principal, we can use the formula: P = Total – I P = 138800 – (0.05)(3)(120000) P = 120,000
- Olufunmi has taken a loan of ₦150,000 with an interest rate of 8% per year for 4 years. The total amount she has to pay back is ₦194,400. To calculate the principal, we can use the formula: P = Total – I P = 194400 – (0.08)(4)(150000) P = 150,000
- Oluseun has a credit card balance of ₦200,000 with an annual interest rate of 10%. How much interest will he pay in 1 year? I = Prt I = (200000)(0.10)(1) I = ₦20,000 P = Total – I P = 200000 – 20000 P = 180000
- Oluwatosin wants to save ₦500,000 in a savings account with an annual interest rate of 2% for 5 years. After 5 years, he has a total of ₦610,000, how much was the principal he deposited? I = Prt I = (500000)(0.02)(5) I = ₦50,000 P = Total – I P = 610000 – 50000 P = 560000
Fill the table.
| S/N | Principal (₦) | Rate (%) | Time (years) | Simple Interest (₦) |
|---|---|---|---|---|
| 1 | 100,000 | 5 | 2 | – |
| 2 | 150,000 | 6 | 3 | – |
| 3 | 200,000 | 8 | 4 | – |
| 4 | 250,000 | 10 | 5 | – |
| 5 | 300,000 | 12 | 6 | – |
Note: you can use the formula I = Prt to calculate the simple interest for each given example above.
Evaluation
- What is the formula for simple interest? a) I = Prt b) I = P/rt c) I = Pr + t d) I = P + rt
- If a person takes out a loan of ₦50,000 at an interest rate of 5% per year for 2 years, how much interest will they pay? a) ₦5,000 b) ₦2,500 c) ₦10,000 d) ₦7,500
- If a person deposits ₦100,000 into a savings account with an annual interest rate of 3% for 4 years, how much interest will they earn? a) ₦12,000 b) ₦9,000 c) ₦15,000 d) ₦6,000
- If a person takes out a loan of ₦150,000 at an interest rate of 6% per year for 3 years, how much will they have to pay back in total? a) ₦169,000 b) ₦195,000 c) ₦180,000 d) ₦162,000
- If a person has a credit card balance of ₦20,000 with an annual interest rate of 15%, how much interest will they pay in 1 year? a) ₦3,000 b) ₦2,500 c) ₦4,000 d) ₦3,500
- If a person wants to save ₦500,000 in a savings account with an annual interest rate of 2%, how many years will it take to reach their goal if they make no additional deposits? a) 20 b) 25 c) 30 d) 35
- If a person deposits ₦200,000 into a savings account with an annual interest rate of 4% for 3 years, how much interest will they earn? a) ₦24,000 b) ₦16,000 c) ₦12,000 d) ₦8,000
- If a person takes out a loan of ₦100,000 at an interest rate of 8% per year for 2 years, how much will they have to pay back in total? a) ₦116,000 b) ₦112,000 c) ₦108,000 d) ₦104,000
- If a person has a credit card balance of ₦30,000 with an annual interest rate of 18%, how much interest will they pay in 1 year? a) ₦5,400 b) ₦4,500 c) ₦6,300 d) ₦3,600
- If a person wants to save ₦600,000 in a savings account with an annual interest rate of 3%, how many years will it take to reach their goal if they make no additional deposits? a) 20 b) 25 c) 30 d) 35
Discount: Discount is a reduction in the original price of a product or service. It can be offered for various reasons, such as for early payment or bulk purchase. Discounts are typically expressed as a percentage of the original price.
- Olusegun buys a laptop that is priced at ₦100,000 and is offered a 10% discount. He will pay: ₦100,000 x 10/100 = ₦10,000 less.
- Oludare wants to purchase a phone that is priced at ₦80,000. He is offered a discount of 20%. He will pay: ₦80,000 x 20/100 = ₦16,000 less.
- Olufunmi wants to purchase a dress that is priced at ₦25,000. She is offered a discount of 15%. She will pay: ₦25,000 x 15/100 = ₦3,750 less.
- Oluseun wants to purchase a suit that is priced at ₦50,000. He is offered a discount of 5%. He will pay: ₦50,000 x 5/100 = ₦2,500 less.
- Oluwatosin wants to purchase a refrigerator that is priced at ₦150,000. He is offered a discount of 12%. He will pay: ₦150,000 x 12/100 = ₦18,000 less.
Commission: Commission is a fee that is paid to someone for their service in facilitating a sale or other business transaction. It is typically a percentage of the total sale or transaction amount.
- Olusegun is a sales agent and earns a commission of 5% on the sale of a car for ₦1,000,000. He earns: ₦1,000,000 x 5/100 = ₦50,000
- Oludare is a real estate agent and earns a commission of 7% on the sale of a house for ₦3,000,000. He earns: ₦3,000,000 x 7/100 = ₦210,000
- Olufunmi is a stockbroker and earns a commission of 3% on a stock transaction of ₦500,000. She earns: ₦500,000 x 3/100 = ₦15,000
- Oluseun is a travel agent and earns a commission of 10% on a tour package of ₦800,000. He earns: ₦800,000 x 10/100 = ₦80,000
- Oluwatosin is an insurance agent and earns a commission of 15% on the sale of an insurance policy for ₦200,000. He earns: ₦200,000 x 15/100 = ₦30,000
Evaluation
- What is the formula for calculating discount? a) D = P x R b) D = P x (1-R) c) D = P – R d) D = P / R
- If a product is priced at ₦100,000 and is offered a 10% discount, how much will it cost? a) ₦90,000 b) ₦95,000 c) ₦110,000 d) ₦105,000
- If a product is priced at ₦80,000 and is offered a 20% discount, how much will it cost? a) ₦64,000 b) ₦72,000 c) ₦76,000 d) ₦68,000
- If a product is priced at ₦25,000 and is offered a 15% discount, how much will it cost? a) ₦21,250 b) ₦22,500 c) ₦23,750 d) ₦24,000
- If a product is priced at ₦50,000 and is offered a 5% discount, how much will it cost? a) ₦47,500 b) ₦48,000 c) ₦49,000 d) ₦50,000
- If a car is sold for ₦1,000,000 and a sales agent earns a commission of 5%, how much commission will he earn? a) ₦50,000 b) ₦75,000 c) ₦100,000 d) ₦125,000
- If a house is sold for ₦3,000,000 and a real estate agent earns a commission of 7%, how much commission will he earn? a) ₦210,000 b) ₦140,000 c) ₦105,000 d) ₦70,000
- If a stock transaction is made for ₦500,000 and a stockbroker earns a commission of 3%, how much commission will she earn? a) ₦15,000 b) ₦12,500 c) ₦10,000 d) ₦7,500
- If a tour package is sold for ₦800,000 and a travel agent earns a commission of 10%, how much commission will he earn? a) ₦80,000 b) ₦60,000 c) ₦40,000 d) ₦20,000
- If an insurance policy is sold for ₦200,000 and an insurance agent earns a commission of 15%, how much commission will he earn? a) ₦30,000 b) ₦25,000 c) ₦20,000 d) ₦15,000
Copy and fill the table below
| S/N | Original Price (₦) | Discount Rate (%) | Discounted Amount (₦) | Amount Actually Paid (₦) |
|---|---|---|---|---|
| 1 | 100,000 | 10 | 10,000 | – |
| 2 | 80,000 | 20 | 16,000 | – |
| 3 | 25,000 | 15 | 3,750 | – |
| 4 | 50,000 | 5 | 2,500 | – |
| 5 | 150,000 | 12 | 18,000 | – |
Note: You can use the formula D = P x (1-R) for discount rate and D = P – D for Amount actually paid to calculate the unknown answer for each example above.
| S/N | Original Price (₦) | Commission Rate (%) | Amount of Commission Earned (₦) |
|---|---|---|---|
| 1 | 1,000,000 | 5 | – |
| 2 | 3,000,000 | 7 | – |
| 3 | 500,000 | 3 | – |
| 4 | 800,000 | 10 | – |
| 5 | 200,000 | 15 | – |
Note: You can use the formula C = P x R for commission rate to calculate the unknown answer for each example above.
Lesson Presentation
The lesson is presented step by step
Step 1 :
The class teacher revises the previous lesson which was Commercial Maths : Money Conversion, Profit and Loss
Step 2 :
The class teacher introduces the new topic by taking the following steps
Introduction (5 minutes):
- Begin the lesson by asking students if they have ever taken out a loan or made a deposit in a savings account (if applicable).
- Introduce the topic of simple interest and explain that it is the additional amount of money that is added to a loan or deposit over a certain period of time.
- Introduce the topic of discounts and explain that it is a reduction in the original price of a product or service.
- Introduce the topic of commission and explain that it is a fee that is paid to someone for their service in facilitating a sale or other business transaction.
Step 3 :
He gives the pupils instructions that are related to the topic
Direct Instruction (20 minutes):
- Using the whiteboard, provide students with examples of simple interest calculations. Be sure to include the formula and step-by-step instructions.
- Using the whiteboard, provide students with examples of discount calculations. Be sure to include the formula and step-by-step instructions.
- Using the whiteboard, provide students with examples of commission calculations. Be sure to include the formula and step-by-step instructions.
Step 4 :
The teacher guides the pupils by providing and assigning related tasks to the pupils
Guided Practice (20 minutes):
- Provide students with a handout containing simple interest, discount, and commission problems.
- Assign students to work in small groups to solve the problems.
- Circulate the room to assist students as needed.
Step 5:
He allows the pupils to give their own ideas and contributions and he corrects them when the needs arise
Independent Practice (20 minutes):
- Provide students with additional simple interest, discount, and commission problems to solve individually.
- Allow students to use their calculators and the formulas provided in the handout.
- Monitor student progress and assist as needed.
Step 5:
Conclusion and Rounding up
Closure (5 minutes):
- Review the key concepts of simple interest, discount, and commission with the class.
- Ask students to share one thing they learned during the lesson.
- As a homework, assign some question for them to solve and submit the next day.
Evaluation
Assessment:
- Observe students during independent practice to assess their understanding of the concepts.
- Collect and grade the homework assignment for accuracy and completeness.
Differentiation:
- Provide extra support for students who need additional help by pairing them with a peer tutor or offering one-on-one instruction.
- Challenge advanced students by providing more difficult problems to solve.