$3.$ You observe the following market prices for risk$-$free bonds

Bond Maturity Coupon rate Price

T$-$bill $1$ Year $0\%$ $$97\mathrm{.}5$

Canada Bond $3$ Years $2\mathrm{.}25\%$ $$88\mathrm{.}53$

Canada bond $3$ Years $5\mathrm{.}25\%$ $$96\mathrm{.}57$

$($a$)$ All bonds have a face value of $$100$ and all coupon bonds have annual coupon payments. Use the above information to price the following risk$-$free bonds.

$(1)$ A $3$ year zero$-$coupon bond.

$(2)$ A $2$ year $5\mathrm{.}25\%$ Canada Bond.

$(3)$ A $3$ year $7\mathrm{.}25\%$ Canada Bond.