Suppose the one-year forward \(\$ / \epsilon\) exchange rate is \(\$ 1.26\) per euro and the spot exchange rate is \(\$ 1.2\) per euro. What is the forward premium on euros (the forward discount on dollars)? What is the difference between the interest rate on one-year dollar deposits and that on one-year euro deposits (assuming no repayment risk)?

Understanding the exchange rate is fundamental in finance and economics as it reflects the value of one currency relative to another. It's the price at which one currency can be exchanged for another. For international transactions, travelers, investors, and businesses closely watch the exchange rate as it determines how much of one currency is needed to purchase a certain amount of another.

When we speak of the exchange rate in a textbook problem, such as our given exercise, we are scrutinizing the ratio at which dollars can be exchanged for euros. Here, there's a special focus on the spot and forward exchange rates, which are crucial for determining the forward premium or discount.

The spot rate, a fundamental type of exchange rate, is the price to exchange one currency for another for immediate delivery. In our context, it's defined as the current exchange rate, at which one can instantly buy or sell a currency. For example, if the spot rate of USD to EUR is $1.20, it means you can exchange 1.20 US dollars for 1 euro right now.

This rate is continually fluctuating, influenced by factors such as interest rates, economic stability, and global events. Calculating the forward premium involves comparing the spot rate to the forward rate, which is the essence of our textbook exercise.

The interest rate differential between two currencies plays a crucial role in the foreign exchange market. It is the difference in interest rates offered for depositing the two currencies being compared. An interest rate differential influences currency values and can lead to arbitrage opportunities. For instance, if dollars have a higher interest rate than euros, investors are likely to convert their euros to dollars for the higher return. The differential can also impact forward rates.

In the provided exercise, we equate the interest rate differential with the calculated forward premium since we're assuming no repayment risk and covered interest parity holds. This assumption allows us to infer the expected changes in interest rates based on the forward premium.

Covered Interest Parity (CIP) is a financial theory stating that the exchange rate forward premiums (or discounts) are determined by the interest rate differentials between two currencies. In other words, the difference between the forward and spot exchange rates should be equal to the difference between the interest rates of the two currencies involved.

This theory assumes that investors will lock in higher returns through forward contracts if interest rates are different across countries. CIP is used to prevent arbitrage opportunities—the chance to make a risk-free profit from differing exchange rates. In our exercise, the concept of CIP means that if you know the forward premium, you can calculate the expected interest rate differential between the currencies.