# COMPOUND INTEREST, PROFIT AND LOSS, AND SIMPLE INTEREST

**Subject**:

### MATHEMATICS

**Term:**

First Term

**Week:**

Week 3

**Class:**

JSS 3 / BASIC 9

**Previous lesson: **Pupils have previous knowledge of

### The Theory of Numbers

that was taught in their previous lesson

**Topic:**

**COMPOUND INTEREST**

**Behavioural Objectives:**

At the end of the lesson, learners will be able to

- Explain the concept of Profit and loss (revision)
- Solve simple Mathematics questions on Simple interest (revision)
- Simplify simple questions on Compound interest
- Solve word problems on the topics above.

**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:**

**WEEK 3**

**TOPIC: COMPOUND INTEREST**

**CONTENTS:**

- Profit and loss (revision)
- Simple interest (revision)
- Compound interest
- Word problems.

**PROFIT AND LOSS (REVISION)**

When any transaction is done, we either make a profit or a loss. When an article is sold at a price greater than the price it was bought, then a profit is made. On the other hand, if an article is sold at a price less than the cost, we have made a loss.

The difference between the selling price and the cost of an article is known as profit or loss. If the selling price is more than the cost, it is called profit; if the selling price is less than the cost, it is called loss.

We either gain money or lose money when a transaction is completed. A profit is realized when an item is sold for more than it cost to purchase it. However, if an item is sold for less than it costs, we have made a loss.

Hence,

Profit = selling price – cost price

Loss = Cost price – selling price

In commercial transactions, profit and loss are usually expressed as a percentage of the cost price.

**Evaluation**

1. A shopkeeper sold an article for Rs. 950. Had he sold it for Rs. 1020, he would have gained 10%. By how much percent does he lose?

2. A trader bought some goods at Rs. 15000 and sold them at Rs. 20000. His gain percent is:

3. Find the cost price of an article if the seller gains 20% after selling it at Rs. 5400.

4. A shopkeeper sold two similar items at Rs. 840 each. On one he gained 10% and on the other he lost 10%. His overall gain or loss percent is:

5. Q sold an article for Rs. 630 and thus gained 10%. If he had sold it for Rs. 560, he would have gained 20%. Find his cost price.

6. A man sells an article at a loss of 15%. If he had bought it at 5% less and sold it for Rs. 100 more, he would have gained 5%. The cost price of the article is:

7. A man bought a watch for Rs. 1200 and sold it at Rs. 1440. If he had bought it cheaper by 10% and sold it dearer by 10%, he would have gained 20%. The actual profit percentage is:

8.ram sells an article at a loss of 4%. Had he sold if for Rs. 8 less, he would have gained 10%. Find his cost price.

**Objective questions **

1. A shopkeeper sold an article for Rs. 950. Had he sold it for Rs. 1020, he would have gained 10%. By how much percent does he lose?

a) 1% b) 2% c) 5% d) 8%

2. A trader bought some goods at Rs. 15000 and sold them at Rs. 20000. His gain percent is:

a) 20% b) 25% c) 33 1/3 % d) 40%

3. Find the cost price of an article if the seller gains 20% after selling it at Rs. 5400.

a) Rs. 4800 b) Rs. 5000 c) Rs. 5200 d) Rs. 5500

4. A shopkeeper sold two similar items at Rs. 840 each. On one he gained 10% and on the other he lost 10%. His overall gain or loss percent is:

a) 0% b) 1% c) 2% d) Cannot be determined

5. Q sold an article for Rs. 630 and thus gained 10%. If he had sold it for Rs. 560, he would have gained 20%. Find his cost price.

a) Rs. 490 b) Rs. 500 c) Rs. 510 d) Rs. 520

** **

**Examples:**

- A trader bought a book for N75 and sold it for N What is the profit percent?

Solution

Cost price = N75

Selling price = N86

Profit = selling price – cost price

= N86- N75 = N11

=

= 14.67%

- An article which cost N300 was sold for N225, what is the loss percent?

Solution

Cost price = N300

Selling price = N225

Loss = Cost price – selling price

= 25%

**CLASS ACTIVITY**

- Adamu bought a pair of shoes for N2,000. Find his percentage loss if he sold it for #1 800?
- Find the cost price of each of these selling prices
- N540 at a profit of 25%
- N2,500 at a loss of 15%

** **

**SIMPLE INTEREST (REVISION)**

Interest is a payment given for saving money. It can also be the price paid for borrowing money. When interest is calculated on the basic sum of money saved (or borrowed) it is called Simple Interest. Simple interest (I) is calculated using the formula

; ;

The initial amount is called the Principal (P) (the sum of money saved or borrowed). Rate(R) is the annual rate of interest (given as a percentage).The length of the period in which the principal is used is called the Time (T). The principal plus interest is called the Amount.

** **

**Examples:**

- Find the simple interest on N500 for 4 years at the rate of 5%. What is the amount?

**Solution:**

Principal = N500

Time = 4 years

Rate = 5%

= N100

Amount = Principal + Simple interest

= N500 + N100

= N600

** **

- Calculate the interest rate percent per annum for a loan of N5,862 for 3 years and a repayment of N7,895.

**Solution:**

Amount = N7,895

Principal = N5,862

Time = 3 years

Interest = ?

Rate = ?

But we know that,

Amount = Principal + Interest

Interest = Amount – Principal

= N7, 895 – N5, 862 = N2, 033

** **

** **

** **

**CLASS ACTIVITY**

- Find the simple interest on N800 for 3 years at the rate of 60%.
- Calculate the simple interest on N8,000 for 2 years at 4% per annum.

**COMPOUND INTEREST:**

In compound interest, interest is calculated and added to the principal at the end of each interval, thus the principal increases and so the interest becomes larger for each interval. Most saving schemes give compound interest not simple. The total value at the end of the investment is the compound amount.

Thus,

Compound amount = Compound interest + Principal

**Example:**

- Calculate the compound interest on N6, 000 for 4 years at 10% per annum. What is the compound amount?

**Solution**

First year:

Principal = N6, 000

= N600

Amount at the end of the 1st year = (N6, 000+N600)

= N6, 600

Second year:

Principal = N6, 600

= N660

Amount at the end of the 2nd year = (N6,600+ N660)

= N7,260

Third year:

Principal = N7, 260

= N726

Amount at the end of the 3rd year = (N7, 260+N726)

= N7, 986

Fourth year:

Principal = N7, 986

= N798.60

Amount at the end of the 4th year = (N7, 986+ N798.60) = N8,784.60

Compound amount = N8, 784.60

Compound interest = N8, 784.60 – N6, 000 = N2, 784.00

** **

**CLASS ACTIVITY**

- Find the compound amount and interest on N40, 000 at 15% for 2 years.
- Find the amount that #40 000 becomes if saved for 3years at 6% per annum.

** **

**DEPRECIATION**

Most items such as radios, cars clothing, houses, and electrical goods lose value as time passes. This loss in value is called *depreciation. *Depreciation is usually given as a percentage of the item’s value at the beginning of the year

Example:

- A car costing N680, 000 depreciates by 25% in its first year and 20% in its second year. Find its value after 2 years.

Solution

1st year: value of car is N680, 000

25% depreciation

= N680, 000 – N170,000

= N510, 000

2nd year: value of car is N510,000

20% depreciation

= N510, 000 – N102, 000

=N408, 000

** **

**INFLATION**

Due to rising prices, money loses its value as time passes. Lose in value of money is called *Inflation. *Inflation is usually given as the percentage increase in the cost of buying things from year to the next.

** Example:**

- How long will it take for prices to double if the rate of inflation is 20% per annum?

**Solution:**

Start with an initial cost of 100 units.

Initial cost = 100

**R**ise = 20% of 100

After 1 year, cost = 100 + 20 = 120

Rise

After 2 years, cost = 120 + 24=144

Rise

After 3 years, cost =144+28.8 =172.8

** **

Rise

After 4 years, cost = 172.8 + 34.56

= 207. 36

The cost after 4 years is a little more than double of initial cost. Hence prices will double in just less than 4 years.

** **

**PRACTICE EXERCISE**

- Find the simple interest on the following:
- a) ₦4 500 for 3years at 6% per annum
- b) $680 for 2 ½ years at 5% per annum
- Nkedirim collects a loan of ₦500 000 at an interest rate of 20% per annum, what amount will she pay back at the end of the year?
- Calculate the compound interest and compound amount on £960 000 for 3years at 3% at the end of first year, 4% at the end of second year and 5 ½ % at the end of third year to 2 decimal places
- The price of a house was ₦23 400 000 in 2010. At the end of each year, the price increased by 6%. Find the price of the house after 3years

**ASSIGNMENT**

- At what time will a principal of ₦30 000 yield an interest of ₦5 000 at the rate of 5%?
- Akpan borrowed ₦12 000 at 3% simple interest for 2years. How much will he pay all together?
- Find the principal that yields ₦3000 in 5years at 4% per annum simple interest.
- A person saves ₦3 000 at 4 ½ % compound interest. She adds ₦800 to her amount at the end of each year. Find her total savings after 2 years.
- A new car costs $64 000. It depreciates by 25% in the first year, 20% in the second year, and 15% in each of the following years. Find the value of the cat to the nearest $50 after 4years.

** **

**KEYWORDS**

**Interest****Compound****Inflation****Deflation****Depreciation**

**DEFINE THE FOLLOWING KEYWORDS**

**Interest****Compound****Inflation****Deflation****Depreciation****Appreciation.**

**Interest :**Interest is the cost of borrowing money, typically expressed as a percentage of the amount borrowed. The higher the interest rate, the more expensive it is to borrow money.**II. Compound Interest:**Compound interest is when interest is ch on both the original amount borrowed (the principal) and on any accumulated interest from previous periods. The more often interest is compounded, the higher the total amount of interest charged**.****III. Inflation: Inflation**is a general increase in prices and fall in the purchasing power of money. When inflation is high, each dollar buys fewer goods and services are charged on both the principal (the original amount borrowed) and any accumulated interest from previous periods. The more often interest is compounded, the higher the total amount of interest charged.**Deflation: Deflation**is a general decrease in prices, usually caused by a decrease in the money supply or a reduction in government spending. When deflation occurs, each dollar buys more goods and services than it did before.**Deflation**is the opposite of inflation.**Depreciation**: Depreciation is a decrease in the value of an asset over time due to wear and tear, obsolescence, or other factors. For example, a car that is five years old is worth less than a brand-new car because it has been used and is not as new as the newer car.**Appreciation**: Appreciation is an increase in the value of an asset over time due to market conditions, inflation, or other factors. For example, a house that cost $100,000 ten years ago may be worth $200,000 today because of appreciation.

**PRESENTATION:**

Step 1:

The subject teacher revises the previous topic

Step 2:

He or she 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

**CONCLUSION:**

The subject goes round to mark the pupil’s notes. He does the necessary corrections