Question $6$: Currency Forward Contracts $(2/10)$

Assume there are no transactions costs. The current exchange rate between US dollars and

Euros is $$1\mathrm{.}25$ for $1.$ The continuously compounded US$-$Dollar interest rate is $2\%$ and the

continuously compounded Euro interest rate is $1\%.$

$(1)$ If you want to conduct a currency carry trade, what would you do$?$

$(2)$ What is the $3-$month forward price for $100$ Euros?

$(3)$ Suppose the $3-$month forward price for $100$ Euros is mispriced at $$126,$ how can you

arbitrage?

$(4)$ Suppose a US$-$based multinational firm expects a profit of $$3,500,000$ and $2,500,000$

in $9$ months. How can they use Euro forwards to lock in profits in terms of US dollars?

What is the total profit in terms of US dollars by using Euro forwards?