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Foreign Exchange Rates

9.5 Foreign exchange rates (EMA6V)

Different countries have their own currencies. In England, a Big Mac from McDonald's costs \(\text{£}\,\text{4}\), in South Africa it costs \(\text{R}\,\text{20}\) and in Norway it costs \(\text{48}\) kr. The meal is the same in all three countries but in some places it costs more than in others. If \(\text{£}\,\text{1} =\text{R}\,\text{12,41}\) and \(\text{1} \text{ kr} = \text{R}\,\text{1,37}\), this means that a Big Mac in England costs \(\text{R}\,\text{49,64}\) and a Big Mac in Norway costs \(\text{R}\,\text{65,76}\).

Exchange rates affect a lot more than just the price of a Big Mac. The price of oil increases when the South African rand weakens. This is because when the rand is weaker, we can buy less of other currencies with the same amount of money.

A currency gets stronger when money is invested in the country. When we buy products that are made in South Africa, we are investing in South African business and keeping the money in the country. When we buy products imported from other countries, we are investing money in those countries and as a result, the rand will weaken. The more South African products we buy, the greater the demand for them will be and more jobs will become available for South Africans. Local is lekker!

The three currencies you are most likely to see are the British pound (£), the American dollar (\(\$\)) and the euro (\euro).

This video explains exchange rates and shows some examples of exchange rate calculations.

Video: 2GJ6

Worked example 12: Foreign exchange rates

Saba wants to travel to see her family in Spain. She has been given \(\text{R}\,\text{10 000}\) spending money. How many euros can she buy if the exchange rate is currently \euro{} \(\text{1}\) \(=\)\(\text{R}\,\text{10,68}\)?

Write down the equation

Let the equivalent amount in euros be \(x\)

\begin{align*} x & = \frac{\text{10 000}}{\text{10,68}} \\ & = \text{936,33} \end{align*}

Write the final answer

Saba can buy \euro{} \(\text{936,33}\) with \(\text{R}\,\text{10 000}\).

Exercise 9.6

Bridget wants to buy an iPod that costs \(\text{£}\,\text{100}\), with the exchange rate currently at \(\text{£}\,\text{1}\) \(=\) \(\text{R}\,\text{14}\). She estimates that the exchange rate will drop to \(\text{R}\,\text{12}\) in a month.

How much will the iPod cost in rands, if she buys it now?

Cost in rands = (cost in pounds) \(\times\) exchange rate.

\(=100 \times \frac{14}{1} = \text{R}\,\text{1 400}\)

How much will she save if the exchange rate drops to \(\text{R}\,\text{12}\)?

Cost in rands \(=100 \times \frac{12}{1} = \text{R}\,\text{1 200}\)

So she will save \(\text{R}\,\text{200}\) (Saving \(= \text{R}\,\text{1 400} - \text{R}\,\text{1 200}\))

How much will she lose if the exchange rate moves to \(\text{R}\,\text{15}\)?

Cost in rands \(=100 \times \frac{15}{1} = \text{R}\,\text{1 500}\)

So she will lose \(\text{R}\,\text{100}\) (Loss \(= \text{R}\,\text{1 400} - \text{R}\,\text{1 500}\))

Mthuli wants to buy a television that costs \(\text{£}\,\text{130}\), with the exchange rate currently at \(\text{£}\,\text{1} = \text{R}\,\text{11}\). He estimates that the exchange rate will drop to \(\text{R}\,\text{9}\) in a month.

How much will the television cost in rands, if he buys it now?

\begin{align*} \text{Cost} &= \text{130} \times \text{R}\,\text{11} \\ &= \text{R}\,\text{1 430} \end{align*}

How much will he save if the exchange rate drops to \(\text{R}\,\text{9}\)?

\begin{align*} \text{Cost} &= \text{130} \times \text{R}\,\text{9} \\ &= \text{R}\,\text{1 170} \end{align*}

Therefore the amount he will have saved is: \begin{align*} \text{Saved} &= \text{R}\,\text{1 430} - \text{R}\,\text{1 170} \\ &= \text{R}\,\text{260} \end{align*}

How much will he lose if the exchange rate moves to \(\text{R}\,\text{19}\)?

\begin{align*} \text{Cost} &= \text{130} \times \text{R}\,\text{19} \\ &= \text{R}\,\text{2 470} \end{align*}

Therefore the amount he will lose is: \begin{align*} \text{Loss} &= \text{R}\,\text{2 470} - \text{R}\,\text{1 430} \\ &= \text{R}\,\text{1 040} \end{align*}

Nthabiseng wants to buy an iPad that costs \(\text{£}\,\text{120}\), with the exchange rate currently at \(\text{£}\,\text{1} = \text{R}\,\text{14}\). She estimates that the exchange rate will drop to \(\text{R}\,\text{9}\) in a month.

How much will the iPad cost, in rands, if she buys it now?

\begin{align*} \text{Cost} &= \text{120} \times \text{R}\,\text{14} \\ &= \text{R}\,\text{1 680} \end{align*}

How much will she save if the exchange rate drops to \(\text{R}\,\text{9}\)?

\begin{align*} \text{Cost} &= \text{120} \times \text{R}\,\text{9} \\ &= \text{R}\,\text{1 080} \end{align*}

Therefore the amount she will have saved is: \begin{align*} \text{Saved} &= \text{R}\,\text{1 680} - \text{R}\,\text{1 080} \\ &= \text{R}\,\text{600} \end{align*}

How much will she lose if the exchange rate moves to \(\text{R}\,\text{18}\)?

\begin{align*} \text{Cost} &= \text{120} \times \text{R}\,\text{18} \\ &= \text{R}\,\text{2 160} \end{align*}

Therefore the amount she will lose is: \begin{align*} \text{Loss} &= \text{R}\,\text{2 160} - \text{R}\,\text{1 680} \\ &= \text{R}\,\text{480} \end{align*}

Study the following exchange rate table:

Country

Currency

Exchange Rate

United Kingdom (UK)

Pounds (£)

\(\text{R}\,\text{14,13}\)

United States (USA)

Dollars (\(\$\))

\(\text{R}\,\text{7,04}\)

In South Africa the cost of a new Honda Civic is \(\text{R}\,\text{173 400}\). In England the same vehicle costs \(\text{£}\,\text{12 200}\) and in the USA \(\$ \text{21 900}\). In which country is the car the cheapest?

To answer this question we work out the cost of the car in rand for each country and then compare the three answers to see which is the cheapest. Cost in rands = cost in currency times exchange rate.

Cost in UK: \(\text{12 200} \times \frac{\text{14,13}}{1} = \text{R}\,\text{172 386}\)

Cost in USA: \(\text{21 900} \times \frac{\text{7,04}}{1} = \text{R}\,\text{154 400}\)

Comparing the three costs we find that the car is the cheapest in the USA.

Sollie and Arinda are waiters in a South African restaurant attracting many tourists from abroad. Sollie gets a \(\text{£}\,\text{6}\) tip from a tourist and Arinda gets \(\$ \text{12}\). Who got the better tip?

Sollie: \(6 \times \frac{\text{14,31}}{1} = \text{R}\,\text{84,78}\)

Arinda: \(12 \times \frac{\text{7,04}}{1} = \text{R}\,\text{84,48}\).

Therefore Sollie got the better tip. He got \(\text{30}\) cents more than Arinda.

Yaseen wants to buy a book online. He finds a publisher in London selling the book for \(\text{£}\,\text{7,19}\). This publisher is offering free shipping on the product.

He then finds the same book from a publisher in New York for \(\$ \text{8,49}\) with a shipping fee of \(\$ \text{2}\).

Next he looks up the exchange rates to see which publisher has the better deal. If \(\$ \text{1} = \text{R}\,\text{11,48}\) and \(\text{£}\,\text{1} = \text{R}\,\text{17,36}\), which publisher should he buy the book from?

London publisher: \(\text{7,19} \times \frac{\text{17,36}}{1} = \text{R}\,\text{124,82}\)

New York publisher: \((\text{8,49} + 2) \times \frac{\text{11,48}}{1} = \text{R}\,\text{120,43}\).

Therefore Yaseen should buy the book from the New York publisher.

Mathe is saving up to go visit her friend in Germany. She estimates the total cost of her trip to be \(\text{R}\,\text{50 000}\). The exchange rate is currently \(\text{€}\,\text{1} = \text{R}\,\text{13,22}\).

Her friend decides to help Mathe out by giving her \(\text{€}\,\text{1 000}\). How much (in rand) does Mathe now need to save up?

We first calculate how much Mathe's friend will give her in rands:

\(\text{1 000} \times \frac{\text{13,22}}{\text{1}} = \text{R}\,\text{13 220}\).

Therefore Mathe now needs to save up: \(\text{R}\,\text{50 000} - \text{R}\,\text{13 220} = \text{R}\,\text{36 780}\).

Lulamile and Jacob give tours over the weekends. They do not charge for these tours but instead accept tips from the group. The table below shows the total amount of tips they receive from various tour groups.

GroupTotal tips
British tourists\(\text{£}\,\text{5,50}\)
Japanese tourists\(\text{¥}\,\text{85,50}\)
American tourists\(\$ \text{7,00}\)
Dutch tourists\(\text{€}\,\text{9,70}\)
Brazilian tourists\(\text{40,50}\,\text{BRL}\)
Australian tourists\(\text{9,20}\,\text{AUD}\)
South African tourists\(\text{R}\,\text{55,00}\)

The current exchange rates are:

\begin{align*} \text{£}\,\text{1} & = \text{R}\,\text{17,12} \\ \text{¥}\,\text{1} & = \text{R}\,\text{0,10} \\ \$   \text{1} & = \text{R}\,\text{11,42} \\ \text{€}\,\text{1} & = \text{R}\,\text{12,97} \\ \text{1}\,\text{BRL} & = \text{R}\,\text{4,43} \\ \text{1}\,\text{AUD} & = \text{R}\,\text{9,12} \end{align*}

Which group of tourists tipped the most? How much did they tip (give your answer in rand)?

We need to calculate the value of each tip in rand:

GroupTotal tipsValue of tip in rands
British tourists\(\text{£}\,\text{5,50}\)\(\text{R}\,\text{94,16}\)
Japanese tourists\(\text{¥}\,\text{85,50}\)\(\text{R}\,\text{8,55}\)
American tourists\(\$   \text{7,00}\)\(\text{R}\,\text{79,94}\)
Dutch tourists\(\text{€}\,\text{9,70}\)\(\text{R}\,\text{125,81}\)
Brazilian tourists\(\text{40,50}\,\text{BRL}\)\(\text{R}\,\text{179,42}\)
Australian tourists\(\text{9,20}\,\text{AUD}\)\(\text{R}\,\text{83,90}\)
South African tourists\(\text{R}\,\text{55,00}\)\(\text{R}\,\text{55,00}\)

The Brazilian tourists tipped the most. The rand value of their tip was \(\text{R}\,\text{179,42}\).

Which group of tourists tipped the least? How much did they tip (give your answer in rand)?

The Japanese tourists tipped the least. The rand value of their tip was \(\text{R}\,\text{8,55}\).

Kayla is planning a trip to visit her family in Malawi followed by spending some time in Tanzania at the Serengeti. She will first need to convert her South African rands into the Malawian kwacha. After that she will convert her remaining Malawian kwacha into Tanzanian shilling.

She looks up the current exchange rates and finds the following information:

\begin{align*} \text{R}\,\text{1} & = \text{39,46}\,\text{MWK} \\ \text{1}\,\text{MWK} & = \text{4,01}\,\text{TZS} \end{align*}

She starts off with \(\text{R}\,\text{5 000}\) in South Africa. In Malawi she spends \(\text{65 000}\,\text{MWK}\). When she converts the remaining Malawian kwacha to Tanzanian shilling, how much money does she have (in Tanzanian shilling)?

We first convert from rands to Malawian kwacha: \(\text{5 000} \times \frac{\text{39,46}}{\text{1}} = \text{197 300}\,\text{MWK}\)

She spends \(\text{65 000}\,\text{MWK}\) of this and so she has \(\text{132 300}\,\text{MWK}\) to convert to Tanzanian shillings.

Now we can convert from Malawian kwacha to Tanzanian shillings: \(\text{132 300}\,\text{MWK} \times \frac{\text{4,01}}{\text{1}} = \text{530 523}\,\text{TZS}\)

So she will have \(\text{530 523}\,\text{TZS}\) to spend in Tanzania.