Question

Suppose you observe that 90-day interest rate across the eurozone is 4%, while the interest rate in the U.S. over the same time period is 1%. Further, the spot rate and the 90-day forward rate on the euro are both $1.25. You have $700,000 that you wish to use in order to engage in covered interest arbitrage. After 90-days in the bank, your 560,000 euros will have grown to euros (including interest).

Answer 1

Using covered interest arbitrage with $700,000, the student exchanges it for €560,000 at a rate of $1.25 per euro. After applying the 4% eurozone 90-day interest rate, the resulting amount after interest is €565,600.

Step-by-step explanation:

The student's question asks about the outcome of engaging in covered interest arbitrage with a 90-day interest rate discrepancy between the eurozone and the U.S. A key aspect of the question is to calculate the value of a certain number of euros after they have accrued interest over a 90-day period at a specific interest rate.

The student starts with $700,000 and converts it to euros at the spot rate of $1.25, resulting in €560,000. Using the given 4% eurozone 90-day interest rate, we apply the formula for simple interest: Final Amount = Principal * (1 + (Interest Rate * Time)). Since the interest rate is annual, we adjust the time period to a fraction of the year (90 days = 90/360 = 0.25 year).

Therefore, the calculation will be: €560,000 * (1 + (0.04 * 0.25)) = €560,000 * 1.01 = €565,600. Thus, after 90 days, the €560,000 will have grown to €565,600 including interest.