Today is $\frac{04}{30}\frac{?}{20}.$ You have a unit of commodity to sell in a month, and you would like to lock the price at $$100$ by hedging with futures. Since you are not selling a professionally traded commodity, you take a modified version of futures contract which is marked to the market every week as opposed to every day. The margin account yields $5\mathrm{.}2\%$ per annum compounded weekly, with a margin requirement $($opening balance$)$ of $$40$ and maintenance margin $($minimum balance$)$ of $$20.$ The futures price of the commodity you are selling is $$110$ on $\frac{05}{01},$$$104$ on $\frac{05}{08},$$$98$ on $\frac{05}{15},$$$94$ on $\frac{05}{22},$$$102$ on $\frac{05}{29}.$ Assume you enter the contract today and will make the delivery on $05/30,$ using the $05/29$ price. Assume one year consists of $52$ weeks.

$($a$)(30$ pt$)$ Fill out the cash flow table below, showing all the calculation details for $(1)$ through $(15).$ Profit is the money you receive, so a cash outflow is negative profit.

$\backslash$table$[[$Date$,$Futures Price,Profit,Interest,Balalce$],[\frac{04}{30},$$$100,0,0,$$$40$