Three U$.$S$.$ treasury bonds with a face value of $$100$ are as follows:

Bond A: Maturity $=2$ years; Coupon Rate $=0\%$; Price $=$ $$90\mathrm{.}77$

Bond B: Maturity $=2$ years; Coupon Rate $=5\%$; Price $=$ $$100\mathrm{.}11$

Bond C: Maturity $=3$ years; Coupon Rate $=4\%$; Price $=$ $$93\mathrm{.}98$

Question $1$: Assuming no arbitrage, what is the price of a $1-$year zero$-$coupon bond with a face value of $$100?$

Question $2$: What is the price of a $3-$year $8\%$ coupon bond with face value of $$100?$

Question $3$: The market offers a risk$-$free $3-$year annuity $($annual payments $=$ $$50)$ for $$138.$ What's the price $($no$-$arbitrage$)$ of this annuity?

Question $4$: Create an arbitrage strategy that yields immediate profit using treasury bonds A$,$ B$,$ and C for each annuity bought or sold. Assume one $3-$year annuity. How much should you buy or sell of Bond A$,$ Bond B$,$ and Bond C$?$