Suppose the value of the S&P $500$ stock index is currently $2,000.$Suppose the value of the S&P $500$ stock index is currently $2,000.$

a$)$ If the $1-$year T$-$bill rate is $3\%$ and the expected dividend yield on the S&P $500$ is $2\%,$

what should the $1-$year maturity futures price be$?$

b$)$ What if the $T-$bill rate is less than the dividend yield, for example, $1\%?$

c$)$ What if the contract maturity is $18$ months?