Suppose that the one-year interest rate is 5.0 percent in the United States; the spot exchange rate is $1.20/€; and the one-year forward exchange rate is $1.16/€. What must the one-year interest rate be in the euro zone to avoid arbitrage? A. 5.0% B. 8.62% C. none of the options D. 6.09%

8.62%

Explanation:

Arbitrage refers to a situations whereby currency, commodities, or securities are bought and sold simultaneously in different market with the aim of making profit by taking advantage of different in the prices of the same asset.

From the question, the one-year interest rate be in the euro zone to avoid this arbitrage can be calculated as follows:

1.16 ÷ 1.20 = 1.05 ÷ (1 + R) (1)

Where R denotes one-year interest rate in the euro zone that prevents arbitrage.

From equation (1), we can solve for R as follows:

0.9667 = 1.05 ÷ (1 + R)

0.9667(1 + R) = 1.05

0.9667 + R0.9667 = 1.05

R0.9667 = 1.05 - 0.9667

R0.9667 = 0.0833  

R = 0.0833 ÷ 0.9667

R = 0.0862  or 8.62%

Therefore, the one-year interest rate must be 8.62% in the euro zone to avoid arbitrage.

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