Question

Suppose the U.S. dollar price of a British pound is \(\$ 1.50\); the dollar price of a curo is \(\$ 1\); a hotel room in London, England, costs 120 British pounds; and a comparable hotel room in Hanover, Germany, costs 200 curo. a. Which hotel room is cheaper for a U.S. tourist? b. What is the exchange rate between the euro and the British pound?

Short answer

The hotel room in London, England is cheaper for a U.S. tourist. b. What is the exchange rate between the euro and the British pound? The exchange rate between the euro and the British pound is 1.50 British pounds per euro.

Step-by-step solution

Convert the cost of the hotel rooms to U.S. dollars

To compare the prices of the hotel rooms, we have to convert them to the same currency, which is U.S. dollars in this case. We will use the given exchange rates: Cost of the London hotel room in British pounds: 120 pounds Cost of the Hanover hotel room in euros: 200 euros Exchange rate: 1 British pound = \(\$ 1.50\) Exchange rate: 1 euro = \(\$ 1\) Cost of the London hotel room in U.S. dollars: 120 pounds * \(\$ 1.50\) = \(\$ 180\) Cost of the Hanover hotel room in U.S. dollars: 200 euros * \(\$ 1\) = \(\$ 200\)

Compare the U.S. dollar prices of the hotel rooms

Now that we have the costs of the hotel rooms in U.S. dollars, we can compare them: Cost of the London hotel room in U.S. dollars: \(\$ 180\) Cost of the Hanover hotel room in U.S. dollars: \(\$ 200\) Since \(\$ 180 < \$ 200\), the hotel room in London, England is cheaper for a U.S. tourist.

Find the exchange rate between the euro and the British pound

To find the exchange rate between the euro and the British pound, we can use the given exchange rates with the U.S. dollar: Exchange rate: 1 British pound = \(\$ 1.50\) Exchange rate: 1 euro = \(\$ 1\) Let \(x\) be the exchange rate between 1 euro and British pounds. We can write the equation: 1 euro * \(x\) British pounds = \(\$1.50\) Now solve for \(x\): \(x\) = \(\frac{\$1.50}{\$ 1}\) = 1.50 Therefore, the exchange rate between the euro and the British pound is 1.50 British pounds per euro.

Answer

a. The hotel room in London, England is cheaper for a U.S. tourist. b. The exchange rate between the euro and the British pound is 1.50 British pounds per euro.

Key concepts

Foreign Exchange Market

The foreign exchange market is a global decentralized or over-the-counter market for trading currencies. This financial market determines the exchange rates for every currency.

It includes all aspects of buying, selling, and exchanging currencies at current or determined prices. When U.S. tourists travel abroad, they must engage with this market to exchange their U.S. dollars for the local currency of their travel destination. The rates they receive play a vital role in determining the comparative costs of goods and services in a foreign country.

For instance, if a U.S. tourist wishes to book a hotel in London or Hanover, they would need to know the dollar price of British pounds and euros, respectively. As currency values fluctuate, the cost in U.S. dollars for services abroad can vary, making it imperative for travelers to understand and monitor the foreign exchange market.

Currency Conversion

Currency conversion is the process of exchanging one currency for another. It is based on the current exchange rates provided by the foreign exchange market. Whether for travel, business, or investment purposes, understanding how to convert currencies is vital for making informed financial decisions.

In our exercise, the conversion is straightforward because the exchange rates for GBP (British Pound) and EUR (Euro) to USD (U.S. Dollar) are given. However, real-life conversions might require factoring in transaction fees or different rates for buying and selling. For practice, individuals should master simple conversions like those in the textbook exercise before tackling more complex real-world transactions, where rates can change rapidly due to market forces.

Comparative Cost Analysis

Comparative cost analysis is a financial decision-making tool used to compare the costs of two or more alternatives, taking into account all relevant factors such as exchange rates and unit prices.

In the context of our exercise, to determine which hotel room is more economical for a U.S. tourist, the costs of hotel rooms in London and Hanover are compared in their local currencies, converted to USD for a like-for-like examination.

Cost analysis often involves identifying the most cost-effective option among several competing ones. For students and travelers alike, understanding comparative cost analysis, especially within the framework of different currencies, becomes crucial in planning budgets and making savvy financial choices during international travels or in business scenarios.