# 3.2 Foreign exchange rates

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## Foreign exchange rates - (not in caps, included for completeness)

Is $500 ("500 US dollars") per person per night a good deal on a hotel in New York City? The first question you will ask is “How much is that worth in Rands?". A quick call to the local bank or a search on the Internet (for example on (External Link) ) for the Dollar/Rand exchange rate will give you a basis for assessing the price. A foreign exchange rate is nothing more than the price of one currency in terms of another. For example, the exchange rate of 6,18 Rands/US Dollars means that$1 costs R6,18. In other words, if you have $1 you could sell it for R6,18 - or if you wanted$1 you would have to pay R6,18 for it.

But what drives exchange rates, and what causes exchange rates to change? And how does this affect you anyway? This section looks at answering these questions.

## How much is r1 really worth?

We can quote the price of a currency in terms of any other currency, for example, we can quote the Japanese Yen in term of the Indian Rupee. The US Dollar (USD), British Pound Sterling (GBP) and the Euro (EUR) are, however, the most common used market standards. You will notice that the financial news will report the South African Rand exchange rate in terms of these three major currencies.

 Currency Abbreviation Symbol South African Rand ZAR R United States Dollar USD $British Pounds Sterling GBP £ So the South African Rand, noted ZAR, could be quoted on a certain date as 6,07040 ZAR per USD (i.e.$1,00 costs R6,07040), or 12,2374 ZAR per GBP. So if I wanted to spend $1 000 on a holiday in the United States of America, this would cost me R6 070,40; and if I wanted £1 000 for a weekend in London it would cost me R12 237,40. This seems obvious, but let us see how we calculated those numbers: The rate is given as ZAR per USD, or ZAR/USD such that$1,00 buys R6,0704. Therefore, we need to multiply by 1 000 to get the number of Rands per $1 000. Mathematically, $\begin{array}{ccc}\hfill 1,00& =& \mathrm{R}6,0740\hfill \\ \hfill \therefore \phantom{\rule{3.33333pt}{0ex}}1\phantom{\rule{3.33333pt}{0ex}}000\phantom{\rule{3.33333pt}{0ex}}×\phantom{\rule{3.33333pt}{0ex}}1,00& =& 1\phantom{\rule{3.33333pt}{0ex}}000\phantom{\rule{3.33333pt}{0ex}}×\phantom{\rule{3.33333pt}{0ex}}\mathrm{R}6,0740\hfill \\ & =& \mathrm{R}6\phantom{\rule{3.33333pt}{0ex}}074,00\hfill \end{array}$ as expected. What if you have saved R10 000 for spending money for the same trip and you wanted to use this to buy USD? How many USD could you get for this? Our rate is in ZAR/USD but we want to know how many USD we can get for our ZAR. This is easy. We know how much$1,00 costs in terms of Rands.

$\begin{array}{ccc}\hfill 1,00& =& \mathrm{R}6,0740\hfill \\ \hfill \therefore \phantom{\rule{1.em}{0ex}}\frac{1,00}{6,0740}& =& \frac{\mathrm{R}6,0740}{6,0740}\hfill \\ \hfill \frac{1,00}{6,0740}& =& \mathrm{R}1,00\hfill \\ \hfill \mathrm{R}1,00& =& \frac{1,00}{6,0740}\hfill \\ & =& 0,164636\hfill \end{array}$

As we can see, the final answer is simply the reciprocal of the ZAR/USD rate. Therefore, for R10 000 will get:

$\begin{array}{ccc}\hfill \mathrm{R}1,00& =& \frac{1,00}{6,0740}\hfill \\ \hfill \therefore \phantom{\rule{3.33333pt}{0ex}}10\phantom{\rule{3.33333pt}{0ex}}000×\mathrm{R}1,00& =& 10\phantom{\rule{3.33333pt}{0ex}}000×\frac{1,00}{6,0740}\hfill \\ & =& 1\phantom{\rule{3.33333pt}{0ex}}646,36\hfill \end{array}$

We can check the answer as follows:

$\begin{array}{ccc}\hfill 1,00& =& \mathrm{R}6,0740\hfill \\ \hfill \therefore \phantom{\rule{3.33333pt}{0ex}}1\phantom{\rule{3.33333pt}{0ex}}646,36×1,00& =& 1\phantom{\rule{3.33333pt}{0ex}}646,36×\mathrm{R}6,0740\hfill \\ & =& \mathrm{R}10\phantom{\rule{3.33333pt}{0ex}}000,00\hfill \end{array}$

## Six of one and half a dozen of the other

So we have two different ways of expressing the same exchange rate: Rands per Dollar (ZAR/USD) and Dollar per Rands (USD/ZAR). Both exchange rates mean the same thing and express the value of one currency in terms of another. You can easily work out one from the other - they are just the reciprocals of the other.

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