The no-arbitrage 1-year forward rate in $/€, F($/€) is given by
[tex]F(\$/euro)=S(\$/euro)\times \frac{1+i_\$}{1+i_{euro}} [/tex]
where S($/euro) is the spot exchange rate in $/€, [tex]i_\$[/tex] is the interest rate in the US and [tex]i_{euro}[/tex] is the exchange rate in the Euro zone.
Thus, given that the spot
exchange rate is $1.50/€ and interest rates are 5% apr in the u.s. and
3% apr in the euro zone.
The no-arbitrage 1-year forward rate is given by:
[tex]F(\$/euro)=1.50\times \frac{1+0.05}{1+0.03} \\ \\ =1.50\times \frac{1.05}{1.03} =1.50\times1.019 \\ \\ =\bold{\$1.5291}[/tex]
