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So if for example, the Rand exchange rates were given as 6,71 ZAR/USD and 12,71 ZAR/GBP, does this tell us anything about the exchange rate between USD and GBP?

Well I know that if $1 will buy me R6,71, and if £1.00 will buy me R12,71, then surely the GBP is stronger than the USD because you will get more Rands for one unit of the currency, and we can work out the USD/GBP exchange rate as follows:

Before we plug in any numbers, how can we get a USD/GBP exchange rate from the ZAR/USD and ZAR/GBP exchange rates?

Well,

USD / GBP = USD / ZAR × ZAR / GBP .

Note that the ZAR in the numerator will cancel out with the ZAR in the denominator, and we are left with the USD/GBP exchange rate.

Although we do not have the USD/ZAR exchange rate, we know that this is just the reciprocal of the ZAR/USD exchange rate.

USD / ZAR = 1 ZAR / USD

Now plugging in the numbers, we get:

USD / GBP = USD / ZAR × ZAR / GBP = 1 ZAR / USD × ZAR / GBP = 1 6 , 71 × 12 , 71 = 1 , 894
Sometimes you will see exchange rates in the real world that do not appear to work exactly like this. This is usually because some financial institutionsadd other costs to the exchange rates, which alter the results. However, if you could remove the effect of those extra costs, the numbers would balance again.

If $1 = R 6,40, and £1 = R11,58 what is the $/£ exchange rate (i.e. the number of US$ per £)?

  1. The following are given:

    • ZAR/USD rate = R6,40
    • ZAR/GBP rate = R11,58

    The following is required:

    • USD/GBP rate
  2. We know that:

    USD / GBP = USD / ZAR × ZAR / GBP .
  3. USD / GBP = USD / ZAR × ZAR / GBP = 1 ZAR / USD × ZAR / GBP = 1 6 , 40 × 11 , 58 = 1 , 8094
  4. $ 1,8094 can be bought for £1.

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Investigation : cross exchange rates - alternative method

If $1 = R 6,40, and £1 = R11,58 what is the $/£ exchange rate (i.e. thenumber of US$ per £)?

Overview of problem

You need the $/£ exchange rate, in other words how many dollars must you pay for a pound. So you need £1. From the given information we know that it would cost you R11,58 to buy £1 and that $ 1 = R6,40.

Use this information to:

  1. calculate how much R1 is worth in $.
  2. calculate how much R11,58 is worth in $.

Do you get the same answer as in the worked example?

Fluctuating exchange rates

If everyone wants to buy houses in a certain suburb, then house prices are going to go up - because the buyers will be competing to buy those houses. If there is a suburb where all residents want to move out, then there are lots of sellers and this will cause house prices in the area to fall - because the buyers would not have to struggle as much to find an eager seller.

This is all about supply and demand, which is a very important section in the study of Economics. You can think about this is many different contexts, like stamp-collecting for example. If there is a stamp that lots of people want (high demand) and few people own (low supply) then that stamp is going to be expensive.

And if you are starting to wonder why this is relevant - think about currencies. If you are going to visit London, then you have Rands but you need to “buy" Pounds. The exchange rate is the price you have to pay to buy those Pounds.

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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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