$($All units in US $$.)$ We denote by $P(t,T)$ the time$-$t price of a bond maturing

at $T>t.$ Today $(t=0),$ an investor trades two bonds, one maturing in twelve

months having price $P(0,1)=95,$ and paying $2\%$ coupons, semi$-$annually $($we call

this one a $T_1-$bond$).$ The $T_2-$bond matures in two years, and pays $1\%$ coupons,

semi$-$annually $($price $P(0,2)=90).$ Each of the bonds has a face value of $100.$

The investor decides to purchase a hundred $T_2-$bonds and sell $T_1-$bonds.

$($a$)$ Compute the amount $$ in the bond portfolio so to off$-$set coupon payments

of both bonds within the first year.