Summary Financial Mathematics notes and examples CAPS Grades 10-12

Module 4: Financial Mathematics

CAPS extraction indicating progression from Grades 10-12

Grade 10 Grade 11 Grade 12
Use simple and compound Use simple and compound Calculate the value of n in
growth formulae growth formulae the formula A  P1  i  and
n


A  P1  in  and A  P1  in  and
A  P1  i 
n


A  P1  i  to solve A  P1  i  to solve
n n
Apply knowledge of
problems (including interest, problems (including straight geometric series to solve
hire purchase, inflation, line depreciation and annuity and bond repayment
population growth and other depreciation on a reducing problems.
real life problems). balance) Critically analyse different
The effect of different periods loan options.
of compounding growth and
decay (including effective
and nominal interest rates).


Introduction
The study of Financial Mathematics is centred on the concepts of simple and compound
growth. The learner must be made to understand the difference in the two concepts at Grade
10 level. This may then be successfully built upon in Grade 11, eventually culminating in the
concepts of Present and Future Value Annuities in Grade 12.


One of the most common misconceptions found in the Grade 12 examinations is the lack of
understanding that learners have from the previous grades (Grades 10 and 11) and the lack
of ability to manipulate the formulae. In addition to this, many learners do not know when to
use which formulae, or which value should be allocated to which variable. Mathematics is
becoming a subject of rote learning that is dominated by past year papers and
memorandums which deviate the learner away from understanding the basic concepts,
which make application thereof simple.


Let us begin by finding ways in which we can effectively communicate to learners the
concept of simple and compound growth.



PARTICIPANT HAND-OUT – FET PHASE 1

,Simple and Compound Growth
 What is our understanding of simple and compound growth?
 How do we, as educators, effectively transfer our understanding of these concepts to our
learners?
 What do the learners need to know before we can begin to explain the difference in
simple and compound growth?




A star educator always takes
into account the dynamics
of his/her classroom




The first aspect that learners need is to understand the terminology that is going to be used.


Activity 1: Terminology for Financial Maths
Group organisation: Time: Resources: Appendix:
Groups of 6 30 min  Flipchart None
 Permanent markers
In your groups you will:
1. Select a scribe and a spokesperson for this activity only – should rotate from activity
to activity.

2. Use the flipchart and permanent markers to write down definitions/explanations that
you will use in your classroom to explain to your learners the meaning of the
following terms:

 Interest
 Principal amount
 Accrued amount
 Interest rate
 Term of investment
 Per annum
3. Every group will have an opportunity to provide feedback.


PARTICIPANT HANDOUT – FET PHASE 2

,Notes:
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Now that we have a clear understanding of the terms that we are going to use, let us try and
understand the difference between Simple and Compound growth.

We will make use of an example to illustrate the difference between these two concepts.



Worked Example 1: Simple and Compound Growth
(20 min)
The facilitator will now provide you with a suitable example to help illustrate the difference
between simple and compound growth.


Example 1:
Cindy wants to invest R500 in a savings plan for four years. She will receive 10% interest
per annum on her savings. Should Cindy invest her money in a simple or compound growth
plan?

Solution:

Simple growth plan:

Interest is calculated at the start of the investment based on the money she is investing and
WILL REMAIN THE SAME every year of her investment.
 10 
Interest  500   
 100 
 R50
This implies that every year, R50 will be added to her investment.

Year 1 : R500 + R50 = R550
Year 2 : R550 + R50 = R600
Year 3 : R600 + R50 = R650 N Notice that the
Year 4 : R650 + R50 = R700 interest remains
the same every
year.



PARTICIPANT HAND-OUT – FET PHASE 3

, Cindy will have an ACCRUED AMOUNT of R700. Her PRINCIPAL AMOUNT was R500.

Compound Growth Plan:

The compound growth plan has interest that is recalculated every year based on the money
that is in the account. The interest WILL CHANGE every year of her investment.




Year 1:
 10 
Interest  500   
 100 
 R50
Therefore, at the end of the 1st year Cindy will have R500 + R50 = R550

Year 2:
 10 
Interest  550    N Notice that the interest is
 100  recalculated based on the
 R55 amount present in the
account.


Therefore, at the end of the 2nd year Cindy will have R550 + R55 = R605

Year 3:
 10 
Interest  605    N Notice that the interest is
 100  recalculated based on the
 R60.50 amount present in the
account.

Therefore, at the end of the 3rd year Cindy will have R605 + R60.50 = R665.50

Year 4:
 10 
Interest  665.50    N Notice that the interest is
 100 
recalculated based on the
 R66.55 amount present in the
account.

Therefore, at the end of the 4th year Cindy will have R665.50 + R66.55 = R732.05

Cindy will have an ACCRUED AMOUNT of R732.05. Her PRINCIPAL AMOUNT was R500.




PARTICIPANT HANDOUT – FET PHASE 4