Assume that the euro$-$dollar spot rate, s$,$ is $0\mathrm{.}78$ euro cents per dollar. Also, the corresponding semi$-$annual forward rate, F is $0\mathrm{.}76.$ At the same time, the domestic six$-$month interest rate in the domestic economy $($Europe$)$ is $3\%$ while the corresponding interest rate in America is $4\%.$

$($i$)$ If an investor had $1$ million at his disposal, would you recommend him to invest it in America because of the higher interest rate? Justify your answer.

$($ii$)$ With other data held constant, calculate the amount of the semiannual F dollar forward rate that ensures the effect of the CAE $($Covered Interest Arbitrage$)$ contract?