Arithmetic of Finance (II)

Grade 12 · Mathematics

Semester 1 | Period 2 | Week 9

Download the Lessonotes Mobile Liberia app for faster lesson access on Android and iPhone.

Get it on Google Play Get it on the Apple App Store

Subject: Mathematics

Semester: 1

Period: 2

Week: 9

WEEK 9

Class: Grade 12
Age: 17 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Arithmetic of Finance II
Focus: Amortization, Bonds, Debentures, Shares, Income Tax, Value Added Tax (VAT), and Calculations using Logarithms

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

  1. Define and compute amortization.
  2. Calculate interest on bonds and debentures using logarithms.
  3. Understand and calculate shares, rate of income tax, and value added tax (VAT).
  4. Solve problems in capital markets, including bonds, debentures, shares, taxes, and rates using logarithmic tables.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Problem-solving approach
  • Practical exercises
  • Case studies and discussions

INSTRUCTIONAL MATERIALS:

  • Solution chart for compound interest
  • Solution chart for bonds and debentures
  • Logarithm table
  • Charts for rates, taxes, and VAT calculations
  • Visual aids or diagrams showing capital market processes
  • Guest speaker (optional) from the stock exchange or inland revenue office

 

PERIOD 1: Introduction to Amortization and Capital Markets
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Amortization

Introduces the concept of amortization, explaining it as the process of gradually paying off a debt over time through regular payments. Demonstrates a basic amortization table.

Students listen attentively and ask questions about the definition and concept of amortization.

Step 2 - Concept of Capital Markets

Introduces the types of capital market instruments: bonds, debentures, shares, and their relevance in real-world finance.

Students engage by sharing what they know about bonds, debentures, and shares.

Step 3 - Amortization Table

Demonstrates how to calculate amortization using a sample loan (principal, rate, term). Shows the first few payments in an amortization schedule.

Students take notes and follow the examples in the amortization calculation.

NOTE ON BOARD:

Amortization: The process of paying off debt through regular payments.

  
     

 

EVALUATION (5 exercises):

    
  1. Define amortization.
  2. What is the main difference between bonds and shares?
  3. How is amortization calculated?
  4. What is the formula for amortization?
  5. What is the role of capital markets in an economy?

CLASSWORK (5 questions):

  1. Calculate the monthly amortization for a loan of N100,000 at 5% annual interest for 3 years.
  2. What is the principal in an amortization formula if the payment is N12,000, the interest rate is 6%, and the loan term is 2 years?
  3. Give one real-world example where amortization is used.
  4. What is the effect of increasing the loan term on amortization payments?
  5. Calculate the total amount paid for a loan of N50,000 after 4 years with 8% annual interest, assuming monthly payments.

ASSIGNMENT (5 tasks):

  1. Research the differences between amortization and depreciation.
  2. Find an example of a company that issues bonds, and explain how the company calculates interest on the bonds.
  3. What does the rate of interest on a bond indicate about the market conditions?
  4. Explain how share prices are determined in the capital markets.
  5. Calculate the monthly payment for a loan of N150,000 at 7% annual interest for 5 years.

 

PERIOD 2: Calculation of Interest on Bonds and Debentures
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Bonds and Debentures

Explains bonds and debentures as long-term debt instruments issued by corporations or governments. Introduces the concept of interest on bonds.

Students listen and take notes on the difference between bonds and debentures.

Step 2 - Bond Interest Calculation

Demonstrates how to calculate the interest on bonds using the bond formula and logarithms for compound interest.

Students follow along with the example calculation.

Step 3 - Logarithm Table Usage

Guides students through using a logarithm table to calculate interest and solve compound interest problems for bonds.

Students practice using the logarithm table in pairs to calculate bond interest.

CLASSWORK (5 questions):

  1. A bond has a principal of N100,000, an interest rate of 7% per annum, and a term of 3 years. Calculate the total interest.
  2. How much would you receive after 10 years on a N200,000 bond with 5% annual interest compounded annually?
  3. What is the maturity value of a bond with a 4% interest rate for 6 years on a N30,000 principal?
  4. Calculate the interest for a debenture of N50,000 at an interest rate of 8% for 4 years.
  5. A bond is sold at a 10% interest rate. What will be the interest after 2 years on N75,000?

ASSIGNMENT (5 tasks):

  1. Calculate the compound interest for a bond of N150,000 at 6% annual interest for 8 years.
  2. What are the advantages of issuing bonds over debentures?
  3. How do interest rates affect the price of a bond?
  4. What is the present value of a bond with a 5% interest rate and a principal of N200,000 after 7 years?
  5. Research the taxation of bond interest in your country and explain its implications.

 

 

 

EVALUATION (5 exercises):

  1. What is a share?
  2. Calculate the dividend for 100 shares if the dividend per share is N5.
  3. Calculate the income tax for a salary of N50,000 with a 10% tax rate.
  4. Calculate the VAT for a product priced at N200 with a 5% VAT rate.
  5. How does VAT affect consumer prices?

CLASSWORK (5 questions):

  1. Calculate the dividend for 200 shares with a dividend of N3 each.
  2. A person earns N80,000 monthly. Calculate their income tax at a 15% rate.
  3. Calculate VAT for an item priced at N500 with a VAT rate of 7%.
  4. If an individual earns N150,000 annually, calculate their income tax at a 20% rate.
  5. What is the price of a product including VAT if the price is N1,000 and the VAT rate is 10%?

ASSIGNMENT (5 tasks):

  1. Research the taxation rates for income and VAT in your country.
  2. Calculate the dividend for 500 shares with a dividend of N8 per share.
  3. Calculate the income tax for a salary of N120,000 at a 25% rate.
  4. Calculate the VAT for a product priced at N1,200 with a 12% VAT rate.
  5. Discuss the implications of income tax and VAT on businesses and consumers.

 

PERIOD 4: Application of Logarithms to Financial Problems
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Logarithms in Finance

Explains the importance of logarithms in solving financial problems such as compound interest and bond interest.

Students listen and take notes on logarithms' role in finance.

Step 2 - Guided Practice

Provides sample problems for students to solve using logarithms, focusing on financial calculations.

Students solve problems in groups or pairs with teacher guidance.

Step 3 - Independent Practice

Allows students to independently solve additional problems using logarithms.

Students complete practice problems and seek assistance when needed.

 

PERIOD 5: Review and Practical Problem Solving
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity
     

Step 1 - Recap of Key Concepts

Reviews the main points covered during the week: amortization, bonds, debentures, shares, taxes, VAT, and logarithms.

Students ask questions about any unclear concepts.

Step 2 - Group Problem Solving

Guides students through solving a comprehensive financial problem that integrates all topics covered.

Students work in groups to solve a complex problem.

Step 3 - Class Discussion

Facilitates a class discussion on real-life applications of the topics learned.  Students engage in a discussion on the practical applications of mathematics in finance. |

 

EVALUATION: Students will complete both written exercises and practical problem-solving tasks to assess their understanding of the lesson content.

 

ASSIGNMENT (Final Task):
Solve a real-world financial problem involving amortization, bonds, shares, and income tax using the techniques learned in this unit. Provide a detailed report with all necessary calculations.