Problem $2\mathrm{.}3$: Equity index $($variation on problem $5\mathrm{.}27$ in Hull$)$ The spot SP$500$ index is $6,080.$ The three$-$month risk$-$free rate is $4\mathrm{.}50\%$ per annum and the dividend yield over the next three months is $2\mathrm{.}0\%$ per annum. The six$-$month risk$-$free rate is $5\mathrm{.}00\%$ per annum and the dividend yield over the next six months is also $2\mathrm{.}0\%$ per annum.

Estimate the futures price of the SP$500$ index for three$-$month and sixmonth contracts. All interest rates and dividend yield are continuously compounded.