2. SPECIFIC AIMS
Vukile Xhego
By the end of the lesson, learners should be able
to:
Define compounded and simple interest
Apply compound and simple interest formulae to
calculate future value of an investment/loan
Appreciate the knowledge of compound and
simple interest in real life situations, e.g:
choosing a better investment/loan offer
3. SPECIFIC AIMS
After the lesson learners will be able to differentiate
They will be able to calculate interest earned
Learners will be able to calculate any variable when
given adequate information
The can find interest; number of years ;future value;
principal amount, etc.
Differentiate between different types of interest rate,
example compounded monthly , semi-annual,
annually, quarterly and so on
Vukile Xhego
between simple interest and compound interest
5. INTRODUCTION
You have to pay back service charge to the lender
Vukile Xhego
This money is paid back to the lender along with
the amount borrowed
Sometimes called the Cost of Money or Interest
6. SIMPLE INTEREST
Interest earned only on original amount
Linear/straight-line increase
Formula
An investment of PV rands growing with simple
interest rate i after n years is worth FV rands:
where;
FV is the future value
PV is the present/principal value
i is the interest rate
n is time in years
Vukile Xhego
FV = PV + PV*in = PV(1 + in)
8. EXAMPLE 1: SOLUTION
Organise information:
PV = R300, i = 10% = 0.1, n = 3yrs, FV =?
Vukile Xhego
We know that:
FV = PV(1 + in) = 300(1 + (0.1)3) = 390
Therefore his investment will be worth R390.00
after 3 years
9. COMPOUND INTEREST
Vukile Xhego
Another bank approaches Steve and claims they
will give him a better offer that will earn him
interest at the same interest rate, but
compounded yearly
10. COMPOUND INTEREST
How much will his invest be worth after the 3
years?
Which investment would you advise Steve to opt
for? Why?
Vukile Xhego
11. COMPOUND INTEREST
This is interest calculated not only on the original
investment but as well as on the interest that has
been earned previously
Exponential growth
An investment of PV rands earning interest at
an annual rate i compounded m times a year for
a period of n years is worth FV rands:
Vukile Xhego
FV = PV(1+i/m)n*m
12. COMPOUND INTEREST
Where;
FV is the future value
PV is the principal/present value
i is interest rate
n is the period of investment/loan
m is the number of compounding periods in one
year
Vukile Xhego
13. SOLVING STEVE’S PROBLEM
Organise info:
PV = 300, i = 10%, n = 3yrs, m = 1, FV = ?
FV = PV(1+i/m)^n*m
b) Thus this would be the best option. To answer
the why question, let’s look at a table…
Vukile Xhego
Substitute:
FV = 300(1 + 0.1/1)^3(1)
= 399.3
15. SOLVING STEVE’S PROBLEM
Vukile Xhego
Notice that
After first year the growth is the same, however
In simple interest, growth is based on original
amount…linear growth
In Compound interest, growth is based on the new
principal (FV previous period)…exponential growth
16. SOLVING STEVE’S PROBLEM
Vukile Xhego
Thus exponential investment will yield much
better returns than linear investment…a good
option for Steve
