Consider the futures contract written on the S&P $500$ index and maturing in one year. The interest rate is $5\mathrm{.}2\%,$ and the future value of dividends expected to be paid over the next year is $$75.$ The current index level is $3,000.$ Assume that you can short sell the S&P index.

Required:

Suppose the expected rate of return on the market is $10\mathrm{.}4\%.$ What is the expected level of the index in one year?

What is the theoretical no$-$arbitrage price for a $1-$year futures contract on the S&P $500$ stock index?

Suppose the actual futures price is $3,065.$ Is there an arbitrage opportunity here?