Mastering Compound Interest: 10 Examples Explained for JSS 3 Math Students JSS 3 Mathematics Third Term Lesson Notes Week 2
Subject: Mathematics
Class: JSS 3
Term: Third Term
Week: 2
Topic: Compound Interest
Sub-topic: Understanding and Applying Compound Interest
Duration: 1 hour
Behavioural Objectives:
- By the end of the lesson, students should be able to calculate compound interest accurately.
- Students should understand the concept of compounding and its impact on savings.
- Students should identify real-life situations where compound interest is applicable.
Learning Resources and Materials:
- Whiteboard and markers
- Textbooks with compound interest examples
- Calculators
- Worksheets with compound interest problems
Building Background /Connection to prior knowledge:
- Recap on the concept of simple interest and its formula to establish a foundation for understanding compound interest.
- Relate the idea of earning interest on savings accounts to introduce the concept of compound interest.
Embedded Core Skills:
- Critical thinking
- Problem-solving
- Numeracy skills
Content:
10 worked out samples with explanations:
- Sample 1:
- Initial deposit: ₦1000
- Annual interest rate: 5%
- Time: 3 years
- Compounded annually
- Formula: A = P(1 + r/n)^(nt)
- Calculation: A = 1000(1 + 0.05/1)^(1*3)
- Answer: A = 1000(1.05)^3 = ₦1157.63
- Sample 2:
- Initial deposit: ₦2000
- Annual interest rate: 8%
- Time: 2 years
- Compounded semiannually
- Calculation: A = 2000(1 + 0.08/2)^(2*2)
- Answer: A = 2000(1.04)^4 = ₦2166.40
- Sample 3:
- Initial deposit: ₦5000
- Annual interest rate: 10%
- Time: 5 years
- Compounded quarterly
- Calculation: A = 5000(1 + 0.10/4)^(4*5)
- Answer: A = 5000(1.025)^20 = ₦8144.47
- Sample 4:
- Initial deposit: ₦3000
- Annual interest rate: 12%
- Time: 1 year
- Compounded monthly
- Calculation: A = 3000(1 + 0.12/12)^(12*1)
- Answer: A = 3000(1.01)^12 = ₦3360.71
- Sample 5:
- Initial deposit: ₦4000
- Annual interest rate: 6%
- Time: 4 years
- Compounded annually
- Calculation: A = 4000(1 + 0.06/1)^(1*4)
- Answer: A = 4000(1.06)^4 = ₦4843.35
- Sample 6:
- Initial deposit: ₦6000
- Annual interest rate: 7%
- Time: 3 years
- Compounded quarterly
- Calculation: A = 6000(1 + 0.07/4)^(4*3)
- Answer: A = 6000(1.0175)^12 = ₦7312.83
- Sample 7:
- Initial deposit: ₦8000
- Annual interest rate: 9%
- Time: 2 years
- Compounded semiannually
- Calculation: A = 8000(1 + 0.09/2)^(2*2)
- Answer: A = 8000(1.045)^4 = ₦9397.04
- Sample 8:
- Initial deposit: ₦7000
- Annual interest rate: 4%
- Time: 5 years
- Compounded annually
- Calculation: A = 7000(1 + 0.04/1)^(1*5)
- Answer: A = 7000(1.04)^5 = ₦8221.68
- Sample 9:
- Initial deposit: ₦9000
- Annual interest rate: 11%
- Time: 3 years
- Compounded quarterly
- Calculation: A = 9000(1 + 0.11/4)^(4*3)
- Answer: A = 9000(1.0275)^12 = ₦13336.16
- Sample 10:
- Initial deposit: ₦10,000
- Annual interest rate: 8%
- Time: 4 years
- Compounded monthly
- Calculation: A = 10000(1 + 0.08/12)^(12*4)
- Answer: A = 10000(1.0066667)^48 = ₦13102.67
These examples show how to calculate compound interest over different periods using the compound interest formula. 📊
Evaluation :
- Compound interest is when you earn interest on both the ________ and on the interest that money earns over time.
- a) initial amount
- b) final amount
- c) monthly deposit
- d) bank statement
- If you deposit ₦1000 into a bank account with 5% interest per year, in the first year you’ll earn ________ interest.
- a) ₦50
- b) ₦5
- c) ₦100
- d) ₦500
- Compound interest helps your money grow ________ over time.
- a) slower
- b) at a constant rate
- c) faster
- d) at the same pace
- The formula for compound interest is A = P(1 + r/n)^(nt), where A is the ________.
- a) amount of money accumulated after n years
- b) initial deposit
- c) bank balance
- d) annual interest rate
- In the formula for compound interest, P represents the ________.
- a) amount of money accumulated after n years
- b) initial deposit
- c) annual interest rate
- d) number of years
- If you deposit ₦2000 at 8% interest compounded annually for 3 years, what will be the total amount after 3 years?
- a) ₦2240
- b) ₦2304
- c) ₦2160
- d) ₦2048
- Compound interest is important because it helps your savings grow ________ over time.
- a) slowly
- b) at the same rate
- c) at a constant pace
- d) faster
- The number of times interest is compounded per year is represented by the letter ________ in the compound interest formula.
- a) r
- b) n
- c) t
- d) P
- If you deposit ₦5000 at 6% interest compounded semiannually for 2 years, what will be the total amount after 2 years?
- a) ₦5658
- b) ₦5300
- c) ₦5100
- d) ₦5050
- What does the ‘r’ represent in the compound interest formula?
- a) Number of times compounded per year
- b) Principal amount
- c) Annual interest rate
- d) Number of years
- If you deposit ₦3000 at 12% interest compounded quarterly for 1 year, what will be the total amount after 1 year?
- a) ₦3360
- b) ₦3120
- c) ₦3240
- d) ₦3280
- Compound interest helps your money grow faster over time because you’re earning interest on both your initial deposit and on the interest it ________.
- a) loses
- b) earns
- c) borrows
- d) spends
- What does ‘A’ represent in the compound interest formula?
- a) Amount of money accumulated after n years
- b) Initial deposit
- c) Annual interest rate
- d) Number of times compounded per year
- If you deposit ₦4000 at 4% interest compounded monthly for 2 years, what will be the total amount after 2 years?
- a) ₦4368
- b) ₦4168
- c) ₦4048
- d) ₦4088
- In compound interest, you earn interest on both the initial amount of money you deposited and on the ________ that money earns over time.
- a) principal
- b) expenses
- c) profits
- d) interest
Class Activity Discussion :
- What is compound interest?
- Compound interest is when you earn money not only on the original amount you deposited but also on the interest that money earns over time.
- How does compound interest work?
- It helps your money grow faster because you earn interest on both your initial deposit and the interest it accumulates.
- What’s the formula for compound interest?
- The formula is A = P(1 + r/n)^(nt), where A is the total amount, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
- Why is compound interest important?
- It allows your savings to grow faster over time, helping you reach your financial goals sooner.
- How often can interest be compounded?
- Interest can be compounded annually, semiannually, quarterly, or monthly, depending on the terms of the investment or loan.
- Can compound interest work against you?
- Yes, if you have loans or debts with compound interest, it can accumulate quickly, making it harder to pay off.
- What’s the difference between compound interest and simple interest?
- Compound interest earns interest on both the initial amount and the interest earned over time, while simple interest only earns interest on the principal amount.
- Is compound interest always beneficial?
- Yes, if you’re saving or investing money, compound interest can help it grow faster over time.
- Does compound interest apply to both savings and loans?
- Yes, compound interest applies to both savings accounts and loans, but the effect is different depending on whether you’re earning or paying interest.
- Can compound interest make a small amount of money grow significantly over time?
- Yes, even a small initial deposit can grow into a substantial amount over time due to the power of compound interest.
- What happens if I withdraw money from a compound interest account?
- Withdrawing money reduces the amount of interest you earn because there’s less money left to accumulate interest.
- How can I calculate compound interest without a formula?
- You can use online calculators or mobile apps designed for compound interest calculations.
- Can compound interest be negative?
- Yes, if the interest rate is negative, it means you’re losing money over time instead of gaining it.
- Is compound interest the same as investing?
- Compound interest is one aspect of investing, but investing involves various strategies and risks beyond just earning interest on savings.
- Can compound interest help me reach my financial goals faster?
- Yes, by saving or investing regularly and letting compound interest work for you, you can accelerate your progress towards financial goals like buying a house or retiring comfortably.
Presentation:
Step 1: The teacher revises the previous topic, “Simple Interest,” by asking students to recall the formula and how it works. Understanding how compound interest works and its applications JSS 3 Mathematics Third Term Lesson Notes Week 1
Step 2: The teacher introduces the new topic, “Compound Interest,” by explaining that it’s when interest is earned not only on the initial deposit but also on the interest accrued over time.
Step 3: The teacher encourages students to share their understanding of compound interest and any questions they may have. The teacher corrects any misconceptions and provides additional explanations as needed.
Teacher’s Activities:
- Reviewing the concept of simple interest.
- Explaining the concept of compound interest using examples and diagrams.
- Demonstrating how to use the compound interest formula to solve problems.
- Facilitating class discussions and answering questions.
Learners’ activities:
- Participating in discussions.
- Asking questions for clarification.
- Solving compound interest problems individually and in groups.
- Presenting their solutions to the class.
Assessment:
- Observing students’ participation in class discussions and their ability to solve compound interest problems.
- Reviewing completed worksheets for accuracy.
- Asking questions during the lesson to gauge understanding.
Evaluation questions:
- What is compound interest?
- How does compound interest differ from simple interest?
- What’s the formula for compound interest?
- How often can interest be compounded?
- Can compound interest work against you? How?
- Give an example of a real-life situation where compound interest is applicable.
- If you deposit ₦5000 at 8% interest compounded annually for 3 years, what will be the total amount after 3 years?
- What happens if you withdraw money from a compound interest account?
- How can compound interest help you reach your financial goals faster?
- What are some strategies for maximizing compound interest earnings?
Conclusion:
- The teacher goes round to mark students’ work and provides necessary corrections.
- Reinforce key concepts and encourage students to continue practicing compound interest problems to improve their understanding.