FINANCIAL MATHEMATICSSimple and Compound interest

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SPECIFIC AIMS

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

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SPECIFIC AIMS

After the lesson learners will be able to differentiate

between simple interest and compound interest

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

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INTRODUCTION

When you borrow money from someone

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INTRODUCTION

You have to pay back service charge to the lender

This money is paid back to the lender along with the amount borrowed

Sometimes called the Cost of Money or Interest

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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:

FV = PV + PV*in = PV(1 + in) where;

FV is the future value PV is the present/principal value i is the interest rate n is time in years

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EXAMPLE

Steve invested R 300 on an account which pays 10% simple interest. How much will his investment be worth after 3 years?

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EXAMPLE 1: SOLUTION

Organise information: PV = R300, i = 10% = 0.1, n = 3yrs, FV =?

We know that: FV = PV(1 + in) = 300(1 + (0.1)3) = 390 Therefore his investment will be worth

R390.00 after 3 years

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COMPOUND INTEREST

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

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COMPOUND INTEREST

How much will his invest be worth after the 3 years?

Which investment would you advise Steve to opt for? Why?

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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:

FV = PV(1+i/m)n*m

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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

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SOLVING STEVE’S PROBLEM

Organise info: PV = 300, i = 10%, n = 3yrs, m = 1, FV = ? FV = PV(1+i/m)^n*m

Substitute: FV = 300(1 + 0.1/1)^3(1) = 399.3

b) Thus this would be the best option. To answer the why question, let’s look at a table…

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SOLVING STEVE’S PROBLEMR300 INVESTED AT 10% P.A

Year Simple interest Compound interest

1 R300 + R30 = R330 R300 + R30 = R330

2 R330 + R30 = R360 R330 + R33 = R363

3 R360 + R30 = R390 R363 + R36.3 = R399.3

4 R390 + R30 = R420 R399.3 + R39.93 = R438.96

5 R420 + R30 = R450 R438.96 + R43.90 = R482.86

100 R3300 R4134183.70195

R300 invested at 10% p.a

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SOLVING STEVE’S PROBLEM 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

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SOLVING STEVE’S PROBLEM

Thus exponential investment will yield much better returns than linear investment…a good option for Steve

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SOLVING STEVE’S PROBLEM

A good option for YOU too…

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REFERENCES

Iniego D. (2014): http://www.slideshare.net/IniegoDianne/compound-interest-29921929?qid=b1cbfc82-2060-4cc5-aad0-b82ce0100578&v=default&b=&from_search=1 Itutor. (2013) : http://www.slideshare.net/itutor/compound-interest-26220842 Bruce C. (2010) : http://www.slideshare.net/brucecoulter/lesson-4-compound-interest-2009 Mike Glenon (2012): http://www.slideshare.net/glennontech/simple-interest-vs-compound-interest?qid=03f1d1bf-4878-41ac-84d8-82f9c9b3ace9&v=qf1&b=&from_search=1#btnNext Mahapatra H.S. (2013) : http://www.slideshare.net/hisema/simple-and-compound-interest-24834757?qid=03f1d1bf-4878-41ac-84d8-82f9c9b3ace9&v=qf1&b=&from_search=3

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REFERENCE

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