You just bought a one$-$year futures contract on the stock of Brandex, a company that pays no dividend. The risk$-$free rate is $5\mathrm{.}25\%$ per year. The stock is currently trading at $$335$ per share.

a$.$ According to the spot$-$futures parity theorem, what should be the price of the futures contract today?

b$.$ Nine months later, the stock price in the spot market drops by $2\mathrm{.}9\%.$ What should be the price of the futures contract at that time?