$($All units in US S$.)$ We denote by $P(t,T)$ the time$-$t price of a bond maturing at $T>t.$ Today $)=(0,$ an investon trades two bonds, one maturing in twelve: months having price $P(0,1)=95,$ and paving $2$ ; coupons, semi$-$anmually $($we call this one a $T_1-$bond$).$ The $T_2-$bond mettures in two scars, and pays $18$ coupons, semi$-$annually $($price $P(0,2)=90..$ Eath of the bonds has a face value of $100.$ The investor decides to purchase a hnndned. T$-$londs and sell $$ T$,-$bonds.

$($a$)$ Compute the amount $$ in the boud portiflid so to off$-$set coupon payments of both bonds within the first wean:

$($b$)$ Compute and illustrate thr cash$-$flows of this bond portfolio wntil $T_2=2.$

$($c$)$ Compare this bond portfolio withl a forwhed rate agreement contracted today. so to pay $5000$ s at $T_h$ for receivins $3N$ at $T_2.($Please compane the costs of these agreements, as well as thein senu$-$funual cash$-$fiows up to $2$ years. You do not need to know the exact wilue of N$.$ Which is cloce to $5000,$ but cannot be computed exactly without knowing the zepo rates.$)$