Today is May $5,2017$ and the current $($APR form$)$ three$-$month interest rate is $r_{0,3mth}=10\%.$ A bank makes a market in $$\frac{95}{\text{\$}}100$ August $2017$ bear put spreads on $10-$year Treasury notes with a semi$-$annual coupon rate of $6\%.$ Specifically, if you long this bear spread from the bank, then you effectively

buy one put on T$-$notes with strike $$100$ and premium $$5,$ and

sell one put on T$-$notes with strike $$95$ and premium $$3.$

Both options are European and mature on August $5,2017.$ There is no bid$-$ask spread or any other transaction costs and the current T$-$Bond price is $$99.$

Suppose you long this bear spread.

$($a$)$ How much money will you pay or receive today?

$($b$)$ What is the maximum payoff at maturity?

$($c$)$ For which bond price$($s$)$ will you receive the maximum payoff?

$($d$)$ Are there any margin requirements for you?