# 2.1 Simple interest

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## Being interested in interest

If you had R1 000, you could either keep it in your wallet, or deposit it in a bank account. If it stayed in your wallet, you could spend it any time you wanted. If the bank looked after it for you, then they could spend it, with the plan of making profit from it. The bank usually “pays" you to deposit it into an account, as a way of encouraging you to bank it with them, This payment is like a reward, which provides you with a reason to leave it with the bank for a while, rather than keeping the money in your wallet.

We call this reward "interest".

If you deposit money into a bank account, you are effectively lending money to the bank - and you can expect to receive interest in return. Similarly, if you borrow money from a bank (or from a department store, or a car dealership, for example) then you can expect to have to pay interest on the loan. That is the price of borrowing money.

The concept is simple, yet it is core to the world of finance. Accountants, actuaries and bankers, for example, could spend their entire working career dealing with the effects of interest on financial matters.

In this chapter you will be introduced to the concept of financial mathematics - and given the tools to cope with even advanced concepts and problems.

Interest

The concepts in this chapter are simple - we are just looking at the same idea, but from many different angles. The best way to learn from this chapter is to do the examples yourself, as you work your way through. Do not just take our word for it!

## Simple interest

Simple Interest

Simple interest is where you earn interest on the initial amount that you invested, but not interest on interest.

As an easy example of simple interest, consider how much you will get by investing R1 000 for 1 year with a bank that pays you 5% simple interest. At the end of the year, you will get an interest of:

$\begin{array}{ccc}\hfill \mathrm{Interest}& =& R1\phantom{\rule{3.33333pt}{0ex}}000×5%\hfill \\ & =& R1\phantom{\rule{3.33333pt}{0ex}}000×\frac{5}{100}\hfill \\ & =& R1\phantom{\rule{3.33333pt}{0ex}}000×0,05\hfill \\ & =& R50\hfill \end{array}$

So, with an “opening balance" of R1 000 at the start of the year, your “closing balance" at the end of the year will therefore be:

$\begin{array}{ccc}\hfill \mathrm{Closing Balance}& =& \mathrm{Opening Balance}+\mathrm{Interest}\hfill \\ & =& \mathrm{R}1\phantom{\rule{3.33333pt}{0ex}}000+\mathrm{R}50\hfill \\ & =& \mathrm{R}1\phantom{\rule{3.33333pt}{0ex}}050\hfill \end{array}$

We sometimes call the opening balance in financial calculations the Principal , which is abbreviated as $P$ (R1 000 in the example). The interest rate is usually labelled $i$ (5% in the example), and the interest amount (in Rand terms) is labelled $I$ (R50 in the example).

So we can see that:

$I=P×i$

and

$\begin{array}{ccc}\hfill \mathrm{Closing Balance}& =& \mathrm{Opening Balance}+\mathrm{Interest}\hfill \\ & =& P+I\hfill \\ & =& P+\left(P×i\right)\hfill \\ & =& P\left(1+i\right)\hfill \end{array}$

This is how you calculate simple interest. It is not a complicated formula, which is just as well because you are going to see a lot of it!

## Not just one

You might be wondering to yourself:

1. how much interest will you be paid if you only leave the money in the account for 3 months, or
2. what if you leave it there for 3 years?

It is actually quite simple - which is why they call it Simple Interest .

1. Three months is 1/4 of a year, so you would only get 1/4 of a full year's interest, which is: $1/4×\left(P×i\right)$ . The closing balance would therefore be:
$\begin{array}{ccc}\hfill \mathrm{Closing Balance}& =& P+1/4×\left(P×i\right)\hfill \\ & =& P\left(1+\left(1/4\right)i\right)\hfill \end{array}$
2. For 3 years, you would get three years' worth of interest, being: $3×\left(P×i\right)$ . The closing balance at the end of the three year period would be:
$\begin{array}{ccc}\hfill \mathrm{Closing Balance}& =& P+3×\left(P×i\right)\hfill \\ & =& P×\left(1+\left(3\right)i\right)\hfill \end{array}$

can someone help me with some logarithmic and exponential equations.
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Salomon
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it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
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I got X =-6
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oops. ignore that.
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