Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pr...
Module 4: Financial Mathematics
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.
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:
• Select a scribe and a spokesperson for this activity only – should rotate from activity
to activity.
• 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.
Notes:
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 10REMAIN THE SAME every year of her investment.
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
Year 4 : R650 +
R50 = R700
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:
Interest 10
500
100
R50
Therefore, at the end of the 1st year Cindy will have R500 + R50 = R550
Year 2:
Interest 10
550
Notice that the interest is
R55
100
recalculated based on the amount present in the account.
Therefore, at the end of the 2nd year Cindy will have R550 + R55 = R605
Notice that the interest is recalculated based on the amount present in the account.
Therefore, at the end of the 3rd year Cindy will have R605 + R60.50 = R665.50
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