A stock index currently stands at $100.$ The continuously compounded risk$-$free interest rate is $8\%.$ The dividend yield is $3\%.$ For simplicity, take $1$ month$=1/12$ years.

$($a$)$ What should the price of a $6-$month prepaid forward contract on the index be$?$

$($b$)$ If the market prepaid forward price of the contract is $98\mathrm{.}8,$ how can you make an arbitrage profit?