Simple and Compound Interest

Learning Objectives

I know the difference between simple and compound interest

I am able to apply the principle of compounding to 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

PercentageThis 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%

A percentage is a

proportion of a

number. It is

represented as a

number out of one

hundred. The word

percent can be

separated into per-

and –cent. Per-

means over, cent

means 100. Percent

therefore means

over 100.

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 understandInterest Rate

This is the 10% in the scenario. The percentage of the principal amount that will be added on to the principal amount.

PeriodThis is the representation of time period.

Present ValueThis is the amount of money you owe or have paid at the present time.

i

Principal Amount

This is the R50 000 in the scenario. The actual amount of money you borrowed.

P

n PV

This is how we denote each of these concepts

P Principal Amount

i Interest Rate

n Period

PV Present Value

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

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.

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.

70 000

65 000

60 000

55 000

50 000

0 1 2

rand

n

Principal amount

Simple interest model: linear relationship

Compound interest model: exponential

relationship

At this point, the linear relationship and the

exponential relationship are equal.

Simple and Compound Interest

With simple interest the money or repayment

increases by the same amount(R5 000) each year.

With compound interest the money or repayment increases by an increasing

amount each year. Between year 0 and 1 it’s R5 000, between year 1 and 2 it’s R 5

500.

Simple Interest•With simple interest, you add the same amount each year of the given period of repayment.

•So in our example, we will take 10% of the principal amount(R50 000) which is R5 000.

•We will add this R5 000 to whatever repayment we make each year for the 5 years.

•The situation in the scenario presented in the previous slides represents simple interest.

Compound Interest•With compound interest, you add a percentage of interest of the amount in the previous term of repayment.

•So in our example, we will begin by taking 10% of the principal amount which is R5 000.

•Then we will add this on to the principal amount to get R55 000. Then we take 10% of this amount(R5 500) and add it on to the R55 000. Etc…

•The following table will illustrate.

Let’s assume a repayment amount of R 10 000 per year

n 0 1 2 3 4 5

Compound Interest

- R5 000 R5 500 R 6 050 R 6655 7320.50

R50 000

R55 000 R 60 500 R66 550 R73 205 -

Total Repaymen

t

R55 000 R 60 500 R66 550 R 73 205 R80 525.50

Simple Interest

- R 5 000 R5 000 R5 000 R5 000 R5 000

R50 000

R55 000 R60 000 R65 000 R70 000 -

Total Repaymen

t

R55 000 R60 000 R65 000 R70 000 R 75 000

x 10% x 10%

x 10%

x 10%x 10%+ +++ +

Simple and 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.THANKFULLY,

Simple InterestFormulas

PV= P(1+ni)

Present Value equals the

principal value multiplied

by (1 plus the period we

want times interest rate).

Compound InterestPV= P(1+i)n

Present Value equals the principal value multiplied by (1 plus the interest rate to the power if the period we are interested in evaluating).

The reason why we use 1+i and 1+ni instead of just i and ni is because i is a fraction(because it is a percentage), and

if you multiply a number by a fraction, it decreases the quantity of a number. So adding 1 makes sure that the number does not decrease to its proportion, but has it’s

proportion added on to it.

Work out the PV of the example using both

simple and compound interest. Use the

formulas with the 1 in them and then take the 1 out and compare your

findings.

STOPTake 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

•With simple depreciation, you calculate 10% of the value on the principal amount

•Each year you deduct the same amount from the total

Compound depreciation

•With compounded depreciation, you calculate 10% of the value of the principal amount

•You then subtract this from your principal amount

•The following year you calculate 10% of the present value you have and deduct that from the total. Etc.

n 1 2 3 4 5

Compound depreciatio

n

R 5000 R4500 R4050 R3645 R3319.50

Total Value R45 000 R40 500 R36 450 R 33 195 R29 875.50

Simple depreciatio

n

R5000 R5000 R5000 R5000 R5000

Total Value R45 000 R40 000 R35 000 R30 000 R25 000

10% 10%10% 10%- ---

Depreciation

Compounded depreciation doesn’t really make much sense so, simple

depreciation is used for the calculation of depreciation.

Simple depreciation

PV=P(1-ni)Compounded depreciation

PV=P(1-i)n

Quick Quiz

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

Instructions:1. Write on a clean piece of

paper2. Keep the paper clean and neat

until Saturday3. Answer all questions

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