On January \(1,2002,\) there were 15 member countries in the European Union. Twelve of those countries eliminated their own individual currencies and began using a new common currency, the euro. For a three-year period from January \(1,1999,\) through December \(31,2001,\) these 12 countries priced goods and services in terms of both their own currencies and the euro. During that period, the values of their currencies were fixed against each other and against the euro. So during that time, the dollar had an exchange rate against each of these currencies and against the euro. The following table shows the fixed exchange rates of four European currencies against the euro and their exchange rates against the U.S. dollar on March 2,2001 . Use the information in the following table to calculate the exchange rate between the dollar and the euro (in euros per dollar) on March 2 , \(2001 .\) $$ \begin{array}{l|r|r} \hline \text { Currency } & \begin{array}{c} \text { Units per } \\ \text { Euro (fixed) } \end{array} & \begin{array}{c} \text { Units per U.S. Dollar } \\ \text { (as of March 2, 2001) } \end{array} \\ \hline \text { German mark } & 1.9558 & 2.0938 \\ \hline \text { French franc } & 6.5596 & 7.0223 \\ \hline \text { Italian lira } & 1,936.2700 & 2,072.8700 \\ \hline \text { Portuguese escudo } & 200.4820 & 214.6300 \\ \hline \end{array} $$

Step by step solution

01

Choose Any Currency

Choose one of those four currencies provided in the table. For instance, let's use the Italian lira.

02

Calculate Dollar to Euro Rate

Use the provided exchange rates to derive the exchange rate for dollars to euros by dividing the units per U.S Dollar by the units per Euro. For Italian Lira this means \(\frac{2,072.8700}{1,936.2700} = 1.0707\) euros per dollar.

03

Validate the Result

To ensure that the derived exchange rate is accurate, this calculation can be repeated using another currency from the table, say the German mark. By dividing the units per U.S. Dollar to the units per Euro for German Mark \(\frac{2.0938}{1.9558} = 1.0707\) euros per dollar. Since it matches with the previously calculated result, it suggests that the exchange rate is accurate.

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