Arithmetic of Finance – SS3 Mathematics Lesson Note (First Term)

Arithmetic of finance deals with money calculations over time. In this lesson, students calculate simple and compound interest, find the depreciation of an item (the loss of its value over time), and find the amount of an annuity, which is the total of equal periodic payments plus the interest they accumulate.

Behavioural objectives

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

• Calculate simple interest given the principal, rate and time.
• Calculate compound interest using the formula.
• Determine the depreciation value of an item.
• Compute the annuities in a given problem.

Instructional resources

• Financial magazines
• Currencies

Lesson presentation

Step 1: Identification of prior ideas

Mode: Individual

Teacher’s role: The teacher asks the students to state the formula for compound interest.

Students’ role: The students answer the questions according to the teacher’s instructions.

Step 2: What are depreciation and annuity?

Mode: Entire class

Teacher’s role: The teacher explains depreciation and annuity to the students.

• Depreciation is a situation in which an item loses value over some time. The amount of decrease every year is called the depreciation charge.
• An annuity is a sequence of equal periodic deposits.
• The annuity due is the payment made at the commencement of the agreed interval.
• The term of the annuity is the period between the commencement of the first payment interval and the last payment interval.

Students’ role: The students listen to their teacher and ask questions where necessary.

Step 3: How do you solve depreciation problems?

Mode: The whole class

Teacher’s role: The teacher leads the students to solve these problems.

Example 1

A small electricity generating set costing ₦30000 loses its value by 20% during the first year and 15% in the second year. Calculate its value at the end of the second year.

Solution

End of the first year, value = ₦30000 – 20% of ₦30000
= ₦30000 – ₦6000
= ₦24000

End of the second year, value = ₦24000 – 15% of ₦24000
= ₦24000 – ₦3600
= ₦20400

Example 2

During every financial year, the value of a machine depreciates by 10%. Find the original value (cost) of a machine which depreciates by ₦2250 during the second year.

Solution

Let the original cost of the machine be ₦x.
Depreciation during the 1st year = 10% of ₦x = ₦0.1x
Value of the machine at the beginning of the second year = ₦x – ₦0.1x = ₦0.9x
Depreciation during the second year = 10% of ₦0.9x = ₦0.09x
Depreciation during the second year = ₦2250
0.09x = 2250
x = ₦25000

Therefore, the original cost of the machine is ₦25000.

Students’ role: The students participate actively.

Step 4: How do you find the amount of an annuity?

Mode: Whole class

Teacher’s role: The teacher leads the students to solve this problem.

The sum of all payments plus the accumulated interest is called the amount of the annuity.

Formula: A = P × [(1 + r)ⁿ – 1] / r

where P = the deposit in naira made at each payment, r = the interest rate per payment period, and n = the number of payment periods.

Example

Calculate the amount of an annuity of ₦3500 payable yearly for 25 years at 10% per annum compounded annually.

Solution

A = P × [(1 + r)ⁿ – 1] / r, where P = ₦3500, r = 10% = 0.1, n = 25
A = ₦3500 × [(1.1)²⁵ – 1] / 0.1
A = ₦3500 × 98.35
= ₦344214.71

Students’ role: The students participate by writing what is on the board.

Evaluation

Mode: The whole class

Teacher’s role: The teacher drills the students to solve this problem.

Find the amount of an annuity of ₦2000 payable yearly for 30 years at 15% per annum compounded annually.

Students’ role: The students solve the problem.

Assignment

1. Find the amount of an annuity of ₦55400 payable yearly for 43 years at 9% per annum compounded annually.
2. Calculate the amount of an annuity of ₦1500 for 2 years at 15% compounded annually.
3. A housewife paid ₦2000.00 for a small transistor radio. The value of the radio depreciates by 6% in the first year and 4% in the second year. Calculate its value at the end of the second year.

Reference books

• New General Mathematics for SS3
• New Concept Mathematics for SS3
• Multipurpose Mathematics for SSCE