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 opportunities?Group of answer choices5.0%6.09%none of the options8.62%
Question
Suppose that the one-year interest rate is 5.0 percent in the United States. The spot exchange rate is 1.16/€. What must the one-year interest rate be in the euro zone to avoid arbitrage opportunities?Group of answer choices5.0%6.09%none of the options8.62%
Solution
To avoid arbitrage opportunities, the interest rates and exchange rates must satisfy the Interest Rate Parity (IRP) condition. The IRP condition is given by the formula:
(1 + i_US) = (1 + i_EU) * (F/S)
where:
- i_US is the interest rate in the US (5.0% or 0.05 in decimal form)
- i_EU is the interest rate in the Euro zone (which we are trying to find)
- F is the forward exchange rate ($1.16/€)
- S is the spot exchange rate ($1.20/€)
We can rearrange the formula to solve for i_EU:
i_EU = [(1 + i_US) * (S/F)] - 1
Substituting the given values into the formula:
i_EU = [(1 + 0.05) * (1.20/1.16)] - 1
Solving the equation gives:
i_EU = 0.0862 or 8.62% in percentage form.
So, the one-year interest rate in the euro zone must be 8.62% to avoid arbitrage opportunities.
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