A $15-$month futures contract on an equity index is currently trading at R$3763\mathrm{.}52.$ The underlying index is currently valued at R$3625$ and the continuously compounded risk$-$free rate is $5\%$ per year. Assuming no transaction costs,

a$)$ What continuously$-$compounded dividend yield is implied by the futures contract price $?[3]$

b$)$ A trader on the Johannesburg Stock Exchange believes that the continuouslycompounded dividend yield will be $2\mathrm{.}085\%$ over the next $15$ months.

What is the $15-$month futures contract price induced by the trader belief $?[2\mathrm{.}5]$

c$)$ Based on the trader belief, is there an arbitrage opportunity $?$ If yes, describe the appropriate strategy for the trader to take advantage of this opportunity.