Consider a $5-$month forward contract for which the underlying asset is a stock index with value of $3,518\mathrm{.}6$ and a continuous dividend yield of $1\mathrm{.}1\%.$ Assume the discrete risk$-$free annual interest rate is $3\mathrm{.}5\%.$

a$.$ Determine the no$-$arbitrage forward price.

b$.$ Calculate the value of a short position if $2$ month$($s$)$ later the index changes to $3,518\mathrm{.}6$ and the risk$-$free rate is still $3\mathrm{.}5\%.$