Question

If we know the exchange rate between Country A's currency and Country B's currency and we know the exchange rate between Country B's currency and Country Cs currency, then we can compute the exchange rate between Country A's currency and Country C's currency. a. Suppose the exchange rate between the Japanese yen and the U.S. dollar is currently \(¥ 115=\$ 1\) and the exchange rate between the British pound and the U.S. dollar is \(£ 0.75=\$ 1 .\) What is the exchange rate between the yen and the pound? b. Suppose the exchange rate between the yen and the dollar changes to \(¥ 120=\$ 1\) and the exchange rate between the pound and the dollar changes to \(£ 0.70=\$ 1\). Has the dollar appreciated or depreciated against the yen? Has the dollar appreciated or depreciated against the pound? Has the yen appreciated or depreciated against the pound?

Short answer

a. The exchange rate between the Yen and Pound is £0.75/¥115. b. The Dollar has appreciated against both the Yen and the Pound. The Yen has appreciated against the Pound.

Step-by-step solution

Calculate the exchange rate between the Yen and Pound

Since we know the exchange rate between the Yen and Dollar, and the Dollar and Pound, we can calculate the exchange rate between the Yen and Pound. We start from the Yen to Dollar exchange rate which is ¥115 = $1. Making this a rate per dollar gives us 1 Dollar to ¥115. Similarly we have the Pound to Dollar rate as £0.75 = $1 or 1 Dollar is equal to £0.75. Now, if we want to know how much 1 Yen is in Pounds, we convert Yen to Dollar then Dollar to Pound. This gives us, 1 Yen = $1/¥115 = £0.75/¥115.

Find the new Pound to Yen exchange rate

Now, given a new exchange rate between Yen and Dollar, and Dollar and Pound, we do the same calculating step as in Step 1 with new rates. So 1 Yen = $1/¥120 = £0.70/¥120.

Determine appreciation or depreciation

Looking at the changes in rates, we can say a currency has depreciated if we get fewer units of it after conversion and appreciated with more units. Now that we have more Yen per Dollar, it can be said that the Dollar has appreciated against the Yen. Similarly with more Pounds per Dollar, the Dollar has appreciated against Pound too. As for Yen to Pound, with the decrease of Pounds per Yen, it can be concluded that the Yen has appreciated against the Pound.

Key concepts

Currency Appreciation and Depreciation

Understanding the dynamics of currency appreciation and depreciation is crucial when delving into the world of foreign exchange. Fundamentally, a currency appreciates when it increases in value relative to another currency. Conversely, depreciation occurs when a currency loses value compared to another.

For instance, if the exchange rate of the Japanese yen against the U.S. dollar shifts from \(¥115=\$1\) to \(¥120=\$1\), each dollar now buys more yen, implying that the yen has depreciated and the dollar has appreciated. Similarly, if the British pound moves from \(£0.75=\$1\) to \(£0.70=\$1\), the pound has depreciated while the dollar has appreciated. These changes affect purchasing power and can have significant economic impacts, influencing international trade, inflation, and foreign investments.

It is important to note that exchange rates are influenced by various factors including, but not limited to, interest rates, economic stability, and geopolitical events, creating a dynamic and ever-changing market.

Currency Conversion

Currency conversion is the process of exchanging one currency for another and it's an everyday necessity in a globalized economic landscape. It can be conducted through financial institutions, specialized currency converters, or online exchange platforms.

The basic formula for converting one currency to another through an intermediary currency, as shown in the given exercise, involves two rates: for example, converting Japanese yen to British pounds via the U.S. dollar. To find out how many pounds equal one yen, you first find the dollar equivalent of one yen (\(\text{1 Yen} = \text{\$1}/¥115\)) and then convert this to pounds (\(\text{£0.75}/¥115\)).

It is essential to always update calculations as exchange rates fluctuate frequently. Travelers, businesses, and traders must continuously apply these conversions to ensure accurate financial planning and avoid losses due to exchange rate variations.

Foreign Exchange Market

The foreign exchange market, often referred to as 'Forex' or 'FX', is where currencies are traded. This global marketplace is the largest and most liquid financial market, operating 24 hours a day, five days a week, facilitating international trade, and investment by enabling currency conversion.

Participants range from international banks to individual investors, all contributing to the vast volume of transactions processed daily. Currency values fluctuate in this market based on a plethora of factors including economic indicators, market speculation, and global events.

The exchange rates determined in the FX market are essential for the calculation of conversion rates used in international transactions. This market’s volatility demands constant attention and analysis from those involved, as exchange rates can change rapidly, potentially leading to significant profit or loss in transactions or investments.