Suppose that the value of the S&P $500$ stock index is $3,100.$

Required:

If each E$-$mini futures contract $($with a contract multiplier of $$50)$ costs $$30$ to trade with a discount broker, how much is the transaction cost per dollar of stock controlled by the futures contract?

Note: Do not round your intermediate calculations. Round your answer to $5$ decimal places.

If the average price of a share on the NYSE is about $$42,$ how much is the transaction cost per $$typical share$$ controlled by one futures contract?

Note: Do not round your intermediate calculations. Round your answer to $5$ decimal places.

For small investors, a typical transaction cost $($including the bid$-$ask spread$)$ for direct trades in stocks might be about $8$ cents per share. How many times the transactions costs in futures markets is this?

Note: Do not round your intermediate calculations. Round your answer to $2$ decimal places.

a$.$ Transaction cost per dollar $\%$

b$.$ Transaction cost per share

c$.$ Number of times