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Answer: b) 0.40%
For a quote of USD per EUR, IRP is: \[ F = S e^{(r_{USD}-r_{EUR})T} \] Solve for \(r_{USD}\): \[ r_{USD} = r_{EUR} + \frac{1}{T}\ln\left(\frac{F}{S}\right) \] Given: - \(r_{EUR} = 2.50\%\) - \(S = 1.46\) - \(F = 1.40\) - \(T = 2\) \[ r_{USD} = 0.025 + \frac{1}{2}\ln\left(\frac{1.40}{1.46}\right) \approx 0.025 + \frac{1}{2}(-0.04197) \approx 0.0040 \] So the implied U.S. risk-free rate is approximately **0.40%**, which is **B**.
Author: Manit Arora
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Q-166.3. Assume the two-year riskfree interest rate in the Eurozone is 2.50% per annum with continuous compounding. The spot exchange rate between the Euro (EUR) and the US dollar (USD) is $1.46 USD per EUR (i.e., 1.46 EUR/USD). The two-year forward exchange rate is $1.40 USD per EUR (1.40 EUR/USD). According to interest rate parity (IRP), what is the implied two-year risk-free interest rate in the United States?
A
a) 0.00%
B
b) 0.40%
C
c) 0.80%
D
d) 1.20%
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