Final answer:
Estimating the six-month Euro interest rate from the given forward rates requires more data. The forward price of a stock with known dividends and a current stock price can be calculated using the cost-of-carry model, considering the dividends and the risk-free interest rate.
Step-by-step explanation:
The current USD/Euro exchange rate is 1.4000 dollar per euro. The six-month forward exchange rate is 1.3950. With the six-month USD interest rate being 1% per annum continuously compounded, we are to estimate the six-month Euro interest rate. Based on the interest rate parity, if the forward exchange rate is less than the spot exchange rate, the currency with the higher spot rate (in this case, the Euro) should have a lower interest rate compared to the other currency. However, we need more data to provide a precise estimate for the Euro interest rate.
Regarding the stock that is expected to pay a $1 per share dividend in two months and again in five months, and with a stock price of $50 and a continuous compounding risk-free interest rate of 8% per annum, an investor has taken a short position in a six-month forward contract on the stock. The forward price can be calculated using the cost-of-carry model, which factors in the present value of dividends and risk-free rate.