Finance 4

4.1 Introduction EMCAD

In earlier grades simpleinterest and compoundinterest were studied, together with the concept of

depreciation. Nominal and effective interest rates were also described. Since this chapter expands on

earlier work, it would bebest if you revised the work done in Grades 10 and 11.

When you master the techniques in this chapter, you will be able toassess critically how toinvest

your money when youstart working and earning. And when you are looking at applying for abond

from a bank to buy a home, you will confidentlybe able to get out the calculator and work outhow

much you could actually save by making additional repayments. This chapter will provide youwith

the fundamental concepts you will need to manage your finances.

See introductory video:VMgmf at http://www.everythingmaths.co.za

4.2 Finding the Lengthof the Investment or Loan

EMCAE

In Grade 11, we used the Compound Interest formula A = P (1 + i)nto determine the term of the

investment or loan, by trial and error. Remember that P is the initial amount, A is the current amount,

i is the interest rate and n is the number of time units (number of monthsor years). So if we invest an

amount and know whatthe interest rate is, thenwe can work out how long it will take for the money

to grow to the requiredamount.

Now that you have learnt about logarithms, youare ready to work out the proper algebraic solution. If

you need to remind yourself how logarithms work, go to Chapter 2 (on Page 4).

The basic finance equation is:

A = P. (1 +i)n

If you don’t know what A, P , i and n represent, then you should definitely revise thework from Grade

10 and 11.

Solving for n:

A = P (1 +i)n

(1 +i)n = (A/P )

log((1 +i)n) = log(A/P )

n log(1 +i) = log(A/P )

n = log(A/P )/ log(1 +i)

Remember, you do nothave to memorise this formula. It is very easyto derive any time youneed

it. It is simply a matter of writing down what youhave, deciding what youneed, and solving for that

variable.