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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?

Enrichment: 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.

Think about a time where lots of South Africans are visiting the United Kingdom, and other South Africans are importing goods from the United Kingdom. That means there are lots of Rands (high supply) trying to buy Pounds. Pounds will start to become more expensive (compare this to the house price example at the start of this section if you are not convinced), and the exchange rate will change. In other words, for R1 000 you will get fewer Pounds than you would have before the exchange rate moved.

Another context which might be useful for you to understand this: consider what would happen if people in other countries felt that South Africa was becoming a great place to live, and that more people were wanting to invest in South Africa - whether in properties, businesses - or just buying more goods from South Africa. There would be a greater demand for Rands - and the “price of the Rand" would go up. In other words, people would need to use more Dollars, or Pounds, or Euros ... to buy the same amount of Rands. This is seen as a movement in exchange rates.

Although it really does come down to supply and demand, it is interesting to think about what factors might affect the supply (people wanting to “sell" a particular currency) and the demand (people trying to “buy" another currency). This is covered in detail in the study of Economics, but let us look at some of the basic issues here.

There are various factors which affect exchange rates, some of which have more economic rationale than others:

  • economic factors (such as inflation figures, interest rates, trade deficit information, monetary policy and fiscal policy)
  • political factors (such as uncertain political environment, or political unrest)
  • market sentiments and market behaviour (for example if foreign exchange markets perceived a currency to be overvalued and starting selling the currency, this would cause the currency to fall in value - a self-fulfilling expectation).

Foreign exchange

  1. I want to buy an IPOD that costs £100, with the exchange rate currently at £ 1 = R 14 . I believe the exchange rate will reach R 12 in a month.
    1. How much will the MP3 player cost in Rands, if I buy it now?
    2. How much will I save if the exchange rate drops to R 12 ?
    3. How much will I lose if the exchange rate moves to R 15 ?
  2. Study the following exchange rate table:
    Country Currency Exchange Rate
    United Kingdom (UK) Pounds(£) R 14 , 13
    United States (USA) Dollars ($) R 7 , 04
    1. In South Africa the cost of a new Honda Civic is R 173 400 . In England the same vehicle costs £ 12 200 and in the USA $ 21 900 . In which country is the car the cheapest when you compare the prices converted to South African Rand ?
    2. Sollie and Arinda are waiters in a South African restaurant attracting many tourists from abroad. Sollie gets a £ 6 tip from a tourist and Arinda gets $ 12. How many South African Rand did each one get ?

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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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