Amortization, Bonds, Debentures, Shares and Taxes for SS 3

Class: Senior Secondary School 3 (SS3 / SSS3)
Term: 1st Term
Week: 6
Age: 17 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Financial Mathematics
Previous Lesson: Simple Interest, Compound Interest, Depreciation and Annuity
Topic: ARITHMETIC OF FINANCE – II
Subject Matter: Definition and computation of amortization, solving problems in capital market bonds, debentures, shares, income tax, and Value Added Tax (VAT)

Specific Objectives

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

Cognitive Domain:

• Define amortization and explain its computation.
• Identify and explain capital market instruments such as bonds, debentures, and shares.
• Calculate interest or yield on bonds, debentures, and shares.
• Compute income tax using given rates and allowances.
• Calculate Value Added Tax (VAT) on goods and services.

Affective Domain:

• Appreciate the relevance of financial calculations in personal finance and national economy.
• Develop confidence in solving problems related to financial arithmetic.

Psychomotor Domain:

• Accurately apply mathematical formulas to solve problems involving amortization, capital market instruments, income tax, and VAT.
• Use logarithm tables effectively for complex computations where required.

Social Domain:

• Participate actively in class discussions related to financial concepts.
• Collaborate with peers to solve practical financial arithmetic problems.

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:

• Logarithm tables
• Finance charts
• Tax charts
• Calculators

Rationale for the Lesson

This lesson helps students understand important financial concepts that affect their daily lives and the economy. It equips them with the skills to manage personal finances, understand investments, and comprehend how taxes work. This knowledge is important for responsible financial decision-making.

Prerequisite/Previous Knowledge

Students are expected to have prior knowledge of basic arithmetic operations, percentages, simple and compound interest, and an introduction to financial terms.

Lesson Content/Board Summary

ARITHMETIC OF FINANCE – II

Amortization

Amortization is the process of gradually paying off a debt over a period of time through regular, equal payments. Each payment includes both a portion of the principal amount borrowed and the interest accrued.

The formula for calculating the periodic payment (P) for a loan is:

P = [r * PV] / [1 - (1 + r)^-n]

Where:

1. P = Periodic Payment
2. r = Periodic interest rate (annual rate / number of periods per year)
3. PV = Present Value of the loan (principal amount)
4. n = Total number of payments (number of years * number of periods per year)

Example: A loan of N500,000 is to be amortized over 5 years at an annual interest rate of 10%, compounded annually. Calculate the annual payment.

Solution:

Step 1: Identify variables.

1. PV = N500,000
2. r = 10% = 0.1
3. n = 5 years

Step 2: Apply the formula.

P = [0.1 * 500,000] / [1 - (1 + 0.1)^-5]

P = [50,000] / [1 - (1.1)^-5]

P = [50,000] / [1 - 0.620921]

P = [50,000] / [0.379079]

P ≈ N131,897.66

The annual payment is approximately N131,897.66.

Students may also be asked to solve for the present value (loan amount) or the number of payments if other variables are given by rearranging the formula.

Capital Market Instruments

Capital market instruments are financial tools used by companies and governments to raise long-term funds. These include bonds, debentures, and shares.

Bonds

Bonds are debt instruments issued by governments or corporations to borrow money from investors. Bondholders receive regular interest payments (coupon payments) and the principal amount at the bond’s maturity date.

The yield on a bond measures the return an investor gets on the bond.

Yield = (Annual Interest Payment / Bond Price) * 100%

Example: A N1,000 bond pays an 8% annual interest. If the bond is currently trading at N950, calculate the yield.

Solution:

Step 1: Calculate the annual interest payment.

1. Annual Interest = 8% of N1,000 = N80

Step 2: Apply the yield formula.

1. Yield = (N80 / N950) * 100%
2. Yield ≈ 8.42%

The bond yield is approximately 8.42%.

Debentures

Debentures are unsecured long-term debt instruments issued by companies. Unlike bonds, they are not usually backed by specific assets but by the general creditworthiness of the issuer.

Shares (Stocks)

Shares represent units of ownership in a company. Shareholders are part-owners of the company.

The main types of shares are:

1. Ordinary Shares: These give shareholders voting rights and variable dividends, which depend on the company’s profits.
2. Preference Shares: These typically do not carry voting rights but receive fixed dividends before ordinary shareholders.

The dividend yield measures the return an investor gets from dividends relative to the share’s price.

Dividend Yield = (Annual Dividend Per Share / Share Price) * 100%

Example: A company pays a dividend of N2.50 per share. If the current share price is N50, calculate the dividend yield.

Solution:

Step 1: Identify variables.

1. Annual Dividend Per Share = N2.50
2. Share Price = N50

Step 2: Apply the dividend yield formula.

1. Dividend Yield = (N2.50 / N50) * 100%
2. Dividend Yield = 5%

The dividend yield is 5%.

Students may also be asked to calculate the annual interest payment, dividend per share, or the price of the instrument if the yield and other relevant figures are provided by rearranging the formula. Using logarithm tables may be necessary for more complex calculations involving powers or roots, although simple percentage calculations usually do not require them.

Income Tax

Income tax is a compulsory levy imposed by the government on the income of individuals and corporations. It is a major source of government revenue.

Key terms related to income tax:

1. Taxable Income: The portion of an individual’s or company’s income that is subject to tax, after all allowable deductions and exemptions have been applied.
2. PAYE (Pay As You Earn): A system where income tax is deducted directly from an employee’s salary by the employer and remitted to the tax authorities.
3. Tax Rates: The percentage at which income is taxed. Tax rates are often progressive, meaning higher income brackets are taxed at higher rates.

Example: An individual earns a gross annual salary of N1,200,000. Allowable deductions are N200,000. The tax rate is 10% on the first N500,000 of taxable income and 15% on the remainder.

Solution:

Step 1: Calculate Taxable Income.

1. Taxable Income = Gross Annual Salary – Allowable Deductions
2. Taxable Income = N1,200,000 – N200,000 = N1,000,000

Step 2: Calculate tax on the first N500,000 of taxable income.

1. Tax (first bracket) = 10% of N500,000 = N50,000

Step 3: Calculate the remainder of taxable income.

1. Remainder = N1,000,000 – N500,000 = N500,000

Step 4: Calculate tax on the remainder.

1. Tax (second bracket) = 15% of N500,000 = N75,000

Step 5: Calculate Total Income Tax.

1. Total Income Tax = Tax (first bracket) + Tax (second bracket)
2. Total Income Tax = N50,000 + N75,000 = N125,000

The total income tax payable is N125,000.

Questions may also require calculating the taxable income or gross income given the total tax paid and the tax rates.

Value Added Tax (VAT)

Value Added Tax (VAT) is a consumption tax placed on a product whenever value is added at each stage of the supply chain, from production to the point of sale. The consumer ultimately pays the VAT.

In Nigeria, the standard VAT rate is 7.5%.

Formula for calculating VAT amount and total price:

1. VAT Amount = VAT Rate * Original Price
2. Total Price (including VAT) = Original Price + VAT Amount
3. Or Total Price = Original Price * (1 + VAT Rate)

Example: A product costs N5,000 before VAT. Calculate the total price including VAT (at 7.5%).

Solution:

Step 1: Calculate VAT amount.

1. VAT Amount = 7.5% of N5,000
2. VAT Amount = (7.5 / 100) * N5,000 = N375

Step 2: Calculate Total Price.

1. Total Price = Original Price + VAT Amount
2. Total Price = N5,000 + N375 = N5,375

The total price including VAT is N5,375.

Similarly, students might be asked to find the original price of an item given its total price (including VAT) and the VAT rate, by using the formula: Original Price = Total Price / (1 + VAT Rate).

Quick Revision Table

Area	Key Point
Amortization	Amortization is the process of gradually paying off a debt over a period of time through regular, equal payments. Each payment includes both a…
Capital Market Instruments	Capital market instruments are financial tools used by companies and governments to raise long-term funds. These include bonds, debentures, and…
Income Tax	Income tax is a compulsory levy imposed by the government on the income of individuals and corporations. It is a major source of government…
Value Added Tax (VAT)	Value Added Tax (VAT) is a consumption tax placed on a product whenever value is added at each stage of the supply chain, from production to the…

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 reviews the previous lesson on basic financial arithmetic. The teacher then introduces the new topic, "ARITHMETIC OF FINANCE – II," highlighting its relevance to daily financial transactions and investments.

Students’ Activity: Students respond to greetings, recall previous knowledge, and listen attentively to the introduction of the new topic.

Learning Point: Prior financial mathematics knowledge.

Step 2: Amortization

Time: 5 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher defines amortization and explains its concept using simple examples, such as car loans or mortgages. The teacher then writes the formula for calculating periodic payments and demonstrates how to use it with an example, guiding students through each step.

Students’ Activity: Students listen to the explanation, copy the definition and formula, and follow the teacher's steps to solve the example problem, asking questions for clarification.

Learning Point: Amortisation calculation method.

Step 3: Capital Market Instruments (Bonds, Debentures, Shares)

Time: 5 minutes

Teaching Skill: Explanation/Illustration

Teacher’s Activity: The teacher defines and explains different capital market instruments: bonds, debentures, and shares (ordinary and preference). The teacher then provides formulas for calculating yield on bonds and dividend yield on shares, demonstrating with examples and emphasizing the use of logarithm tables for complex calculations if necessary.

Students’ Activity: Students define the terms, copy the formulas and examples, and practice calculating yields, making sure to understand the distinction between the instruments.

Learning Point: Financial mathematics problem-solving methods.

Step 4: Income Tax

Time: 5 minutes

Teaching Skill: Explanation/Problem Solving

Teacher’s Activity: The teacher defines income tax, explains concepts like taxable income, PAYE, and progressive tax rates. The teacher then presents an example problem involving income tax calculation, guiding students through the steps to determine the total tax payable.

Students’ Activity: Students listen, take notes on definitions and concepts, and actively participate in solving the income tax problem, applying the given tax rates and deductions.

Learning Point: Financial mathematics problem-solving methods.

Step 5: Value Added Tax (VAT)

Time: 5 minutes

Teaching Skill: Explanation/Application

Teacher’s Activity: The teacher defines Value Added Tax (VAT), states the standard rate (e.g., 7.5% in Nigeria), and explains how it is applied to goods and services. The teacher works through an example to calculate the VAT amount and the total price of a product including VAT.

Students’ Activity: Students define VAT, note the rate, and follow the steps to calculate VAT and total price, asking questions to ensure understanding.

Learning Point: Financial mathematics problem-solving methods.

Step 6: Class Activity/Practice

Time: 5 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher provides a few short practice questions covering amortization, bond yield, and VAT for students to attempt individually or in pairs. The teacher monitors and offers assistance.

Students’ Activity: Students work on the practice questions, applying the formulas and concepts learned during the lesson.

Learning Point: Financial mathematics problem-solving methods.

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. Define amortization and state the formula for calculating periodic loan payments.
2. Differentiate between bonds and shares.
3. A N2,000 bond pays 10% annual interest. If its market price is N1,800, calculate its yield.
4. An individual has a taxable income of N800,000. If the first N300,000 is taxed at 5% and the remainder at 10%, calculate the total income tax.
5. A product costs N1,200 before VAT. Calculate the total price including VAT at 7.5%.

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 definitions and calculation methods for amortization, capital market instruments, income tax, and VAT. The teacher assigns relevant homework from the textbook.

Students’ Activity: Students listen to the summary, ask any final questions, and copy down the homework assignment.

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 a simple amortisation example using the method taught in the lesson.
2. Explain the difference between a bond and a debenture.
3. Calculate the income from a given number of shares when the dividend per share is provided.
4. Calculate income tax on a stated taxable income using a rate supplied in the question.
5. Calculate VAT on a purchase amount using the rate supplied in the question.

Lesson Keywords

• Amortization – The process of paying off a debt over time with regular payments.
• Bonds – Debt instruments issued by governments or corporations.
• Debentures – Unsecured debt instruments issued by companies.
• Shares – Units of ownership in a company.
• Income Tax – A tax levied by the government on an individual’s or company’s income.
• Value Added Tax (VAT) – A consumption tax on goods and services at each stage of the supply chain.
• Yield – The return on an investment, usually expressed as a percentage.
• Taxable Income – The portion of income subject to taxation.

Differentiation

For struggling learners, the teacher will provide simplified examples and extra guidance during practice sessions. Advanced learners will be given more complex problems and encouraged to explore real-world financial scenarios or research current tax rates and investment opportunities.

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