Transcript Learning Objectives I know the difference between simple and compound interest I am able to apply the principle of compounding to Simple and Compound Interest other fields I know the formula for.

Learning Objectives
I know the difference between simple and
compound interest
I am able
to apply
the principle of compounding
to
Simple
and
Compound
Interest
other fields
I know the formula for calculating simple and
compound interest
I understand the principles of simple and
compound interest
I understand the principles of depreciation
I can apply these principles to unseen problems
Percentage
This circle is
cut into seven
pieces.
The pink pieces
represent two
pieces out of
seven i.e. 2/7 i.e.
28.6%
The yellow pieces
represent four pieces out
of seven i.e. 4/7 i.e. 57.1%
The green piece
represent one
pieces out of seven
i.e. 1/7 i.e. 14.3%
Scenario:
You want to buy a car. The car costs R 50 000. You don’t have the money so
you go to the bank and you ask the bank to borrow you the money.
The bank guy then says:
“Okay, we’ll give you the money but you have
to pay it back over 5 years with a simple interest rate of 10% per year.”
You say:
“What does this actually mean?”
He says:
“ This means that you will pay back the R50 000
over 5 years and pay 10% of the loan added on to that.”
You say:
“I still don’t understand. ”
He says:
“10% of R50 000 is R5 000. You would need to
pay R10 000 every year or 5 years in order for you to have paid the full
amount back in 5 years. With the interest of R5 000 per year you will pay
R15 000 per year. This brings the total repayment to R75 000. ”
You say:
“Oh okay, now I understand!”
Terms you must understand
Principal Amount
This is the R50 000 in
the scenario. The
actual amount of
money you borrowed.
Period
This is the
representation
of time period.
Beware(Watch yourself):
I use the words Principal and
Principle in this topic. Principal
refers to the starting amount.
Principle refers to what we are doing
when we calculate interest.
Interest Rate
This is the 10% in the
scenario. The
percentage of the
principal amount that
be added on to the
eachwill
principal amount.
This is how we denote
of these concepts
P
Principal Amount
i
Interest Rate
n
P Period
i
PV
Present Value
n
PV
Present Value
This is the amount of
money you owe or
have paid at the
present time.
Interest
Linear relationships are
relationships that grow in a
straight line. This means that
interest ,in this case, grows
by the same amount.
Exponential relationships are
relationships that grow in an
exponential way. This means that
interest, in this case, grows by a
percentage of the previous amount.
Interest is the added amount that you need to pay over the amount that
you actually borrowed.
Interest is calculated in two different ways:
Simple interest
Compound interest
Interest is an example of things that grow or increase over time.
Simple interest is a relationship of linear growth.
Compound interest is a relationship of exponential growth.
Simple and Compound Interest
Simple Interest
Compound
Interest
Compound interest
model: exponential
•With simple interest, you
•With compound
interest, you
Let’s assume a repayment amount relationship
add the same amount each
add a percentage of interest of
of R 10 000 per year
year of the given period of
the amount in the previous term
70 000
repayment.
of repayment.
n
0
1
2
3
4
5
rand
65 000
•So
in
our
example,
we
will
•SoR in
our example,
begin
Compound
R5 000
R5 500
6 050
R 6655we will
7320.50
x 10%
x 10%
take 10% of the
principal x 10%
by taking
10%
the principal
x 10% ofinterest
Interest
Simple
60 000
amount(R50
000) which
is
amount
whichR73
is R5
000.
linear
R50 000
R55 000
R 60 500
R66 550model:
205
R5 000.
relationship
55 000
•Then
we
this on
to 525.50
the
Total
R55 000
R 60 500
R66 550 willRadd
73 205
R80
•We will add this R5 000 to
principal amount to get R55 000.
Repayment
50 000
whatever repayment
Then
10%
of this R5 000
Principal
Simple
R we
5 000
R5 000
R5 we
000 take
R5
000
10%the 5
make each year xfor
amount(R5 500) and add it on to
Interest
amount
1
2
years. R50 000 0 R55 000
the
R55
000.
Etc…
R60 000
R65 000
R70 000
-
+
+
n
+
+
+
table
•The
Total situation in theR55 000
R60 000 •The
R65following
000
R70
000will illustrate.
R 75 000
With
compound
interest
the money or
With
simple
interest
the money
At this point, the linear
scenario
presented
in the
Repayment
increases
by the
an increasing
or repayment
relationship and the exponential
previous slides
represents
amount
each
year. Between
same
amount(R5
000) eachyear 0 and 1 it’s
relationship are equal.
simple
interest.
R5 000, between
year. year 1 and 2 it’s R 5 500.
Simple and Compound Interest
Formulas
Simple
Interest
Compound Interest
As you can see, trying to calculate simple interest and
compound interest from tables and graphs can be tedious
and time-consuming and BORING!!!
mathematicians found
formulas that make our lives much much easier.
The reason whyWork
we use
out1+i
theand
PV1+ni
of the
instead of just i and ni is
because i is a fraction(because
example using itboth
is a percentage), and if you
multiply a number
simple
by a fraction,
and compound
it decreases the quantity of a
number. So adding
interest.
1 makes
Use the
sure
formulas
that the number does not
decrease to its proportion,
with the 1 in
but
them
hasand
it’s proportion added on to
then take the 1it.out and
compare your findings.
Take a breathe, and click after
you are sure you understand
the slides preceding this one.
Depreciation
• Depreciation works in the inverse of the
principle of interest.
• Interest describes the increase from the
starting point
• Depreciation describes the
decrease from
the starting point
• With simple depreciation, we calculate the
gradual(linear) decrease from the starting
point
• With compounded depreciation, we calculate
the exponential decrease from th starting
point
Scenario:
After finding out that you will have to pay R30 000 extra on
the car you wanted, you decide to “review” your decision.
One of the things you consider in your “review” is; if the car
is worth R50 000 now, how much will it be worth when you
are done paying for it after 5 years?
You then conduct an investigation. In this you find out the
following:
*Your car will depreciate in value.
*It will depreciate by 10% per annum from the time you first
drive it.
Simple and Compound Depreciation
Simple depreciation
Compound depreciation
•With simple
depreciation, you
ncalculate 10%
1 of the
2
value on the
principalR4500
Compound
R 5000
amount
depreciation
10%
10%
-
Total •Each
Value
R45you
000 deduct
R40 500
year
the same amount from
R5000
Simple
R5000
the total
depreciation
Total Value
R45 000
R40 000
•With compounded
depreciation, you calculate
of the 5
310% of the value
4
principal amount
R4050
R3645
R3319.50
-•You 10%
10%
then subtract
this
from your principal amount
R36 450
R 33 195
R29 875.50
•The following
year you R5000
R5000
R5000
calculate 10% of the
present value you have
that
R35and
000 deduct
R30
000from the
R25 000
total. Etc.
Depreciation
Simple depreciation
Compounded depreciation
Compounded depreciation doesn’t really
make much sense so, simple depreciation
is used for the calculation of depreciation.
Quick Quiz
Instructions:
1. Write on a clean piece of
paper
2. Keep the paper clean and neat
until Saturday
3. Answer all questions
What is the principle of interest
What is simple interest
What is compound interest
What are the formulas for compound and simple interest
In your opinion, which is the better type of interest principle for
businesses
 What is the difference between simple and compounded interest
relationships
 What is the difference between simple and compounded
depreciation relationships





Task
Conduct an investigation of how much
interest would be on a car and what the
repayments would be
Conduct an investigation of how much
the same car would be worth in 72
months with the current market
depreciation rate
Put a teaspoon of yeast in a plastic bag
and leave it on your window seal for the
week, make sure the bag is closed