Question $1.($Futures and Margin Calls$)(65)$ You are a fund manager and would like to trade some S$-$index futures. S$-$index is an equity index. For the S$-$index futures, the maintenance margin is $$11,200,$ and the initial margin is $$12,320.$ Note that the S$-$index futures contract has a contract unit of $50,$ or one S$-$index futures contract has a notional value of $50\backslash$times S$-$Index. The futures price data in the Excel spreadsheet do not take the multiplier $50$ into account.

$(1\mathrm{.}1)$ In this question, you need to compute the varying margin balance of your futures position throughout the three$-$month period from July $3$ to September $29,2023.$ The futures price data is in $[$F$2023$ Midterm.xlsx$](35)$ Suppose you short $3$ futures contracts on July $3,2023.$ Compute the following quantities $($for simplicity, omit the interest you earn in your margin account$)$: i$.$ Daily Gain or Loss: the daily gain or loss to be reflected on your account ii$.$ Account Balance: the margin balance after adjusting for the daily gain and loss iii. Margin Deposit: the amount of new deposit required to meet the margin requirement iv$.$ New Account Balance: the amount in your margin account after placing the margin deposit $2$ v$.$ Total Deposit: the total amount of capital you use to keep the position open $($suppose you never withdraw money from the margin account$)$ vi$.$ Cumulative Profit or Loss

$3-$Jul$-234,492\mathrm{.}25$

$5-$Jul$-234,483\mathrm{.}75$

$6-$Jul$-234,447\mathrm{.}00$

$7-$Jul$-234,434\mathrm{.}00$

$10-$Jul$-234,444\mathrm{.}25$

$11-$Jul$-234,473\mathrm{.}50$

$12-$Jul$-234,507\mathrm{.}50$

$13-$Jul$-234,543\mathrm{.}50$

$14-$Jul$-234,536\mathrm{.}75$

$17-$Jul$-234,553\mathrm{.}75$

$18-$Jul$-234,587\mathrm{.}75$

$19-$Jul$-234,597\mathrm{.}00$

$20-$Jul$-234,565\mathrm{.}50$

$21-$Jul$-234,564\mathrm{.}75$

$24-$Jul$-234,583\mathrm{.}50$

$25-$Jul$-234,596\mathrm{.}00$

$26-$Jul$-234,595\mathrm{.}25$

$27-$Jul$-234,564\mathrm{.}25$

$28-$Jul$-234,606\mathrm{.}50$

$31-$Jul$-234,614\mathrm{.}50$

$1-$Aug$-234,601\mathrm{.}25$

$2-$Aug$-234,537\mathrm{.}25$

$3-$Aug$-234,521\mathrm{.}75$

$4-$Aug$-234,498\mathrm{.}00$

$7-$Aug$-234,537\mathrm{.}75$

$8-$Aug$-234,518\mathrm{.}50$

$9-$Aug$-234,485\mathrm{.}75$

$10-$Aug$-234,485\mathrm{.}75$

$11-$Aug$-234,480\mathrm{.}75$

$14-$Aug$-234,506\mathrm{.}00$

$15-$Aug$-234,454\mathrm{.}00$

$16-$Aug$-234,420\mathrm{.}00$

$17-$Aug$-234,384\mathrm{.}50$

$18-$Aug$-234,382\mathrm{.}75$

$21-$Aug$-234,412\mathrm{.}50$

$22-$Aug$-234,399\mathrm{.}25$

$23-$Aug$-234,447\mathrm{.}00$

$24-$Aug$-234,386\mathrm{.}00$

$25-$Aug$-234,414\mathrm{.}25$

$28-$Aug$-234,442\mathrm{.}25$

$29-$Aug$-234,506\mathrm{.}75$

$30-$Aug$-234,524\mathrm{.}25$

$31-$Aug$-234,516\mathrm{.}00$

$1-$Sep$-234,521\mathrm{.}50$

$5-$Sep$-234,502\mathrm{.}50$

$6-$Sep$-234,471\mathrm{.}50$

$7-$Sep$-234,456\mathrm{.}25$

$8-$Sep$-234,461\mathrm{.}75$

$11-$Sep$-234,490\mathrm{.}25$

$12-$Sep$-234,465\mathrm{.}00$

$13-$Sep$-234,468\mathrm{.}75$

$14-$Sep$-234,506\mathrm{.}00$

$15-$Sep$-234,491\mathrm{.}72$

$18-$Sep$-234,501\mathrm{.}50$

$19-$Sep$-234,490\mathrm{.}00$

$20-$Sep$-234,447\mathrm{.}00$

$21-$Sep$-234,372\mathrm{.}00$

$22-$Sep$-234,361\mathrm{.}00$

$25-$Sep$-234,378\mathrm{.}75$

$26-$Sep$-234,314\mathrm{.}75$

$27-$Sep$-234,313\mathrm{.}50$

$28-$Sep$-234,337\mathrm{.}50$

$29-$Sep$-234,325\mathrm{.}50$

Would you be able to provide examples for each of the calculations as well as the first line off all that needs to be calculated in the table so I can see if I$\text{'}$m on the right path?