$1.$ What is the payoff of a short position on $100$ shares and $50$ long call

options on the stock at a strike price $$100$ with maturity at time T if

$($a$)$ The Stock price at T is $$102$

$($b$)$ The Stock price at T is $$100$

$($c$)$ The Stock price at T is $$97$

$2.$ Draw the payoff as function of S$($T$)$ in problem $1.$

$3.$ Calculate the price of a bond with these characteristics. Assume the

coupon rate is $6\%,$ coupon payments are made every six months $($twice

per year$),$ and the par value $($maturity payment$)$ of the bond is $1,000.$

Years to maturity $=5\mathrm{.}0$;

$($a$)$ if spot interest rate $3\%$ for annual compunding

$($b$)$ if the spot interest rate is $2\%$ for continuous compounding