Consider a $4-$month forward contract for which the underlying asset is a stock index with value of $3,825\mathrm{.}97$ and a continuous dividend yield of $0\mathrm{.}5\%.$ Assume the continuous risk$-$free annual interest rate is $4\mathrm{.}5\%.$

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

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Round your answer to the nearest cent

b$.$ Calculate the value of a long position if $2$ month$($s$)$ later the index changes to $3,825\mathrm{.}97$ and the risk$-$free rate is still $4\mathrm{.}5\%.$

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Round your answer to the nearest cent