Final answer:
The six-month forward rate is calculated using the Interest Rate Parity theory and is approximately US$0.6896 per Australian dollar, which corresponds to option d).
Step-by-step explanation:
The student is asking about the six-month forward exchange rate between the US dollar and the Australian dollar, given the current spot exchange rate, and the six-month risk-free interest rates in both countries with continuous compounding. To calculate the six-month forward rate, we use the Interest Rate Parity (IRP) theory, which states that the forward rate is determined by the spot rate and the difference in interest rates between the two countries.
To find the forward rate (F), we use the formula F = S * e^[(r_d - r_f) * t], where S is the spot rate, r_d is the domestic interest rate (U.S. interest rate in this case), r_f is the foreign interest rate (Australian interest rate), and t is the time in years. In this case, the spot rate S is 0.7000 USD/AUD, the U.S. interest rate r_d is 1% or 0.01, the Australian interest rate r_f is 4% or 0.04, and the time t is 0.5 years (because we are calculating a six-month forward rate).
Plugging the values into the formula, the calculation is F = 0.7000 * e^[(0.01 - 0.04) * 0.5] = 0.7000 * e^(-0.015) = 0.7000 * 0.985111939 = 0.689578259, which means the forward rate is approximately US$0.6896 per Australian dollar, corresponding to option d).