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Learn Maths the fun way
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FINANCIAL MATHEMATICSSimple and Compound interest
Vukile
Xhego
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
Vukile
Xhego
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
Vukile
Xhego
INTRODUCTION
When you borrow money from someone
Vukile
Xhego
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
Vukile
Xhego
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
Vukile
Xhego
EXAMPLE
Steve invested R 300 on an account which pays 10% simple interest. How much will his investment be worth after 3 years?
Vukile
Xhego
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
Vukile
Xhego
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
Vukile
Xhego
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
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
Vukile
Xhego
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
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…
Vukile
Xhego
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
Vukile
Xhego
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
Vukile
Xhego
SOLVING STEVE’S PROBLEM
Thus exponential investment will yield much better returns than linear investment…a good option for Steve
Vukile
Xhego
SOLVING STEVE’S PROBLEM
A good option for YOU too…
Vukile
Xhego
Vukile
Xhego
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
Vukile
Xhego
REFERENCE
Images taken from: Google Images: http//:google.co.za/images
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