Simple Interest, Compound Interest, Depreciation and Annuity for SS 3

Class: Senior Secondary School 3 (SS3 / SSS 3)
Term: 1st Term
Week: 5
Age: 17 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Financial Mathematics
Previous Lesson: Matrices and Surds, Determinants, Inverse and Simplification
Topic: ARITHMETIC OF FINANCE
Subject Matter: Revision of simple interest, compound interest including arithmetic of finance, definition and calculation of depreciation, definition and determination of annuity

Specific Objectives

By the end of the lesson, students should be able to:

Cognitive Domain:

• Recall the formulas for simple and compound interest.
• Define depreciation and annuity.
• Calculate simple interest, compound interest, and depreciation.
• Determine the future value of an ordinary annuity.

Affective Domain:

• Appreciate the importance of financial calculations in daily life.
• Develop an interest in understanding financial concepts.

Psychomotor Domain:

• Accurately apply financial formulas to solve problems.
• Use logarithm tables or calculators effectively for financial computations.

Social Domain:

• Participate in discussions about financial planning.

Reference Materials

The following resources were used in planning this lesson:

• FCT-ERC SS 3 Scheme of Work, September 2014 curriculum.
• Relevant State Unified Scheme of Work.
• A suitable General Mathematics textbook for SS 3.

Instructional Materials

The teacher will teach this lesson with the aid of:

• Finance charts
• Logarithm solution charts
• Bond and debenture charts
• Whiteboard and markers
• Calculators

Rationale for the Lesson

This lesson helps students understand how money grows or diminishes over time, which is important for personal financial planning and making informed economic decisions. It enables them to apply mathematical concepts to real-world financial situations, preparing them for future financial literacy.

Prerequisite/Previous Knowledge

Students have prior knowledge of basic arithmetic operations, percentages, and simple algebraic equations. They may have also been introduced to basic interest calculations in earlier classes.

Lesson Content/Board Summary

ARITHMETIC OF FINANCE

Revision of Simple Interest

Simple interest is the interest calculated only on the initial principal amount. It does not include interest from previous periods.

Formula: I = (P × R × T) / 100

1. I = Simple Interest
2. P = Principal (initial amount)
3. R = Rate of interest per annum (%)
4. T = Time in years

Amount (A) = Principal (P) + Simple Interest (I)

Example 1: Calculate the simple interest on N8,000 for 4 years at 5% per annum.

Steps:

1. Identify the given values: P = N8,000, R = 5%, T = 4 years.
2. Apply the formula: I = (8000 × 5 × 4) / 100.
3. Calculate the interest: I = N1,600.

Example 2: A sum of N15,000 earned a simple interest of N2,250 in 3 years. Find the rate per annum.

Steps:

1. Identify the given values: I = N2,250, P = N15,000, T = 3 years.
2. Rearrange the formula to find R: R = (I × 100) / (P × T).
3. Substitute the values: R = (2250 × 100) / (15000 × 3).
4. Calculate the rate: R = 225000 / 45000 = 5%.

How to find other values:

1. Principal (P) = (I × 100) / (R × T)
2. Rate (R) = (I × 100) / (P × T)
3. Time (T) = (I × 100) / (P × R)

Compound Interest

Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. It means interest earns interest.

Formula for Compound Amount: A = P (1 + R/100)ⁿ

1. A = Compound Amount (total money after ‘n’ periods)
2. P = Principal
3. R = Rate of interest per compounding period (%)
4. n = Number of compounding periods

Compound Interest (CI) = Amount (A) – Principal (P)

Example 1: Calculate the compound amount and compound interest on N20,000 for 3 years at 10% per annum, compounded annually.

Steps:

1. Identify the given values: P = N20,000, R = 10%, n = 3 years.
2. Apply the amount formula: A = 20000 (1 + 10/100)³.
3. Calculate: A = 20000 (1.1)³ = 20000 × 1.331 = N26,620.
4. Calculate compound interest: CI = A – P = 26620 – 20000 = N6,620.

Example 2: A sum of money invested at 8% compound interest per annum amounted to N11,664 in 2 years. Find the principal sum.

Steps:

1. Identify the given values: A = N11,664, R = 8%, n = 2 years.
2. Apply the amount formula: 11664 = P (1 + 8/100)².
3. Simplify: 11664 = P (1.08)² = P × 1.1664.
4. Solve for P: P = 11664 / 1.1664 = N10,000.

NOTE: If compounding is done more frequently (e.g., semi-annually, quarterly), adjust the rate (R) and number of periods (n) accordingly. For example, if compounded semi-annually, R becomes R/2 and n becomes 2n.

Depreciation

Depreciation is the reduction in the value of an asset over time due to wear and tear, obsolescence, or usage.

The following are common methods for calculating depreciation:

1. Straight-Line Method: This method assumes an asset loses an equal amount of value each year.

   Depreciation per annum = (Original Cost – Salvage Value) / Useful Life

   Book Value (after ‘n’ years) = Original Cost – (Annual Depreciation × n)

   Example: A machine costs N100,000 and has a salvage value of N10,000 after 5 years. Calculate the annual depreciation and its book value after 3 years.

   Steps:

   1. Calculate annual depreciation: (100000 – 10000) / 5 = N18,000.
   2. Calculate book value after 3 years: 100000 – (18000 × 3) = 100000 – 54000 = N46,000.
2. Reducing Balance Method (Diminishing Balance Method): Depreciation is calculated as a fixed percentage of the asset’s book value at the beginning of each period. The depreciation amount decreases each year.

   Book Value (after ‘n’ years) = Original Cost × (1 – Rate/100)ⁿ

   Example: A generator costs N250,000 and depreciates at 20% per annum using the reducing balance method. Calculate its value after 2 years.

   Steps:

   1. Calculate value after 1 year: 250000 × (1 – 20/100) = 250000 × 0.8 = N200,000.
   2. Calculate value after 2 years: 200000 × (1 – 20/100) = 200000 × 0.8 = N160,000.
   3. Alternatively, using the direct formula: 250000 × (1 – 0.20)² = 250000 × (0.8)² = 250000 × 0.64 = N160,000.

Annuity

Annuity refers to a series of equal payments made or received at regular intervals over a period of time. These payments can be for investments, loan repayments, or insurance premiums.

The following are types of annuities:

1. Ordinary Annuity: Payments are made at the end of each period.
2. Annuity Due: Payments are made at the beginning of each period.

Future Value of an Ordinary Annuity: This is the total value of a series of payments at a specific future date, assuming a certain interest rate.

Formula: FV = Pmt × [((1 + r)ⁿ – 1) / r]

1. FV = Future Value of the annuity
2. Pmt = Payment made per period
3. r = Interest rate per period (as a decimal)
4. n = Number of periods

Example: Calculate the future value of an ordinary annuity of N5,000 per year for 4 years at an interest rate of 6% per annum.

Steps:

1. Identify the given values: Pmt = N5,000, r = 0.06, n = 4.
2. Apply the formula: FV = 5000 × [((1 + 0.06)⁴ – 1) / 0.06].
3. Calculate (1.06)⁴ ≈ 1.262477.
4. Substitute and calculate: FV = 5000 × [(1.262477 – 1) / 0.06] = 5000 × [0.262477 / 0.06].
5. FV = 5000 × 4.3746 ≈ N21,873.

Quick Revision Table

Area	Key Point
Revision of Simple Interest	Simple interest is the interest calculated only on the initial principal amount. It does not include interest from previous periods. Formula: I =…
Compound Interest	Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. It means…
Depreciation	Depreciation is the reduction in the value of an asset over time due to wear and tear, obsolescence, or usage. The following are common methods…
Annuity	Annuity refers to a series of equal payments made or received at regular intervals over a period of time. These payments can be for investments,…

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction and Recall

Time: 4 minutes

Teaching Skill: Set Induction

Teacher’s Activity: The teacher greets the students and introduces the topic by asking questions related to saving money, borrowing, and the value of assets over time. For example, "What happens to money kept in a savings account?" or "Does a car retain its original value forever?"

Students’ Activity: Students respond to the questions, sharing their ideas about interest and changing asset values.

Learning Point: Prior financial mathematics knowledge.

Step 2: Simple Interest Revision

Time: 5 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher guides students to recall the definition and formula for simple interest. The teacher solves examples on the board, demonstrating how to calculate simple interest and how to find unknown variables like principal, rate, or time.

Students’ Activity: Students recall the simple interest formula, copy the examples, and participate in solving the problems.

Learning Point: Interest calculation methods.

Step 3: Compound Interest

Time: 5 minutes

Teaching Skill: Explanation/Derivation

Teacher’s Activity: The teacher explains compound interest, contrasting it with simple interest. The teacher derives the compound interest formula and demonstrates its application with examples, including how to find the principal amount if the compound amount is given. The teacher also explains how logarithm tables can be used for more complex calculations.

Students’ Activity: Students listen, take notes, ask questions, and practice calculating compound interest using the formula.

Learning Point: Interest calculation methods.

Step 4: Depreciation Calculation

Time: 5 minutes

Teaching Skill: Explanation/Application

Teacher’s Activity: The teacher defines depreciation and explains its importance. The teacher demonstrates how to calculate depreciation using both the straight-line method and the reducing balance method, providing clear examples for each.

Students’ Activity: Students listen, take notes on the definitions and formulas, and follow the examples. They may attempt simple calculations.

Learning Point: Depreciation calculation method.

Step 5: Annuity Definition and Determination

Time: 5 minutes

Teaching Skill: Explanation/Illustration

Teacher’s Activity: The teacher defines annuity and discusses its types (ordinary annuity, annuity due). The teacher focuses on the future value of an ordinary annuity, providing the formula and solving a practical example on the board.

Students’ Activity: Students pay attention, write down the definition and formula, and observe the steps in the example.

Learning Point: Meaning of financial mathematics.

Step 6: Application and Reinforcement

Time: 5 minutes

Teaching Skill: Individual Practice/Reinforcement

Teacher’s Activity: The teacher presents a different financial mathematics problem and asks students to identify the relevant rule or formula before solving it.

Students’ Activity: Students identify the appropriate method, solve the problem independently and check the reasonableness of the answer.

Learning Point: Financial mathematics practical application.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Differentiate between simple interest and compound interest.
2. State the formula for calculating compound amount.
3. Define depreciation and mention two methods of calculating it.
4. What is an annuity?

Students’ Activity: Students answer orally and in writing, showing working or giving examples where the lesson requires it.

Learning Point: Financial mathematics skills assessed.

Step 8: Note-Taking

Time: 8 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides students to copy the essential Board Summary on financial mathematics into their notebooks, drawing attention to the key rules, examples, diagrams or distinctions already taught.

Students’ Activity: Students copy the essential notes carefully into their notebooks and correct any errors in their earlier work.

Learning Point: Financial mathematics notes recorded.

Step 9: Conclusion

Time: 3 minutes

Teaching Skill: Reinforcement/Summarization

Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of understanding financial calculations in everyday life and for future financial literacy.

Students’ Activity: Students ask final questions, copy the summary,.

Learning Point: Financial mathematics concepts consolidated.

Continuous Assessment/Further Study

Type: Practice Exercise

Instruction: Complete the following tasks in your notebook. Show all mathematical working clearly.

1. Calculate the simple interest on ₦80,000 at 6% per annum for 3 years.
2. Find the amount on ₦50,000 invested at 8% compound interest per annum for 2 years.
3. An asset costing ₦240,000 depreciates by 10% per annum. Find its value after one year.
4. Explain the difference between simple interest and compound interest using one numerical example.
5. Calculate an annuity example using the formula and method taught in the Board Summary.

Lesson Keywords

• Simple Interest – Interest calculated only on the principal amount.
• Compound Interest – Interest calculated on the principal and accumulated interest.
• Principal – The initial amount of money invested or borrowed.
• Rate – The percentage at which interest is charged or earned.
• Time – The duration for which money is invested or borrowed.
• Amount – The total sum of principal and interest.
• Depreciation – The reduction in the value of an asset over time.
• Annuity – A series of equal payments made at regular intervals.
• Future Value – The value of an investment or series of payments at a specified future date.

Differentiation

For students who grasp concepts quickly, the teacher can provide more complex problems involving varying compounding periods (e.g., semi-annually, quarterly) or problems requiring the determination of rate or time in compound interest. For students who need more support, the teacher will provide additional guided practice with simpler examples and visual aids, ensuring they understand each step before moving on.

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