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?

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 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.

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.