On a particular day, the September S&P$500$ stock index futures $($think of this as a forward$)$ was priced at $960\mathrm{.}50.$ The S&P index was at $956\mathrm{.}49.$ The contract expires $73$ days later. 

 

a$)$ Assuming continuous compounding, suppose the risk$-$free rate is $5\mathrm{.}96\%$ and the dividend yield on the index is $2\mathrm{.}75\%.$ In the futures overpriced or underpriced? $($ You need to find the theoretical futures price and compare it to the market price$).$ 

 

 

 b$)$ In $20$ days, what would be the value of the contract to the long position when the index is $971($i$.$e$.,$ Sin $20$days $=971)?$ Assume that the continuously compounding risk$-$free rate is still $5\mathrm{.}96$ percent and the dividend yield on the index is $2\mathrm{.}75$ percent.