futures price $($per unit index$)$ is $$2,460\mathrm{.}61.$ An investor takes a short position in $10S$&$P500$

futures contracts. Suppose the investor is required to deposit a $10\%$ initial margin and that

the maintenance margin is set to $80\%$ of the initial marginal. The margin balance earns a

continuously compounded interest rate of $3\%.$ If the futures price of S&P $500$ index on the

first $5$ days are respectively

Calculate the margin balances at the close of each day. What is the total profit if closing on

Day $5?$ You can perform the calculations using Excel and attach your spread sheet.

$(2$ pts$)$ One investor buys a $1-$year European call option with strike price $K.$ The premium is

$3\mathrm{.}20.$ Another investor buys a European put option with strike price $K+10.$ The premium

is $3\mathrm{.}80.$ At expiry, the stock price is $55.$ The annual effective risk$-$free interest rate is $0\mathrm{.}03.$

Determine $K$ for which both investors make the same profit.

$(1$ pts