Problem $2$ Currently the yield curve observed in the market is as follows: $y_1=6\%,$

$y_2=7\%,$ and $y_3=9\%.$ You are choosing between a two$-$year and three$-$year maturity bonds

all paying annual coupons of $8\%,$ once a year. You strongly believe that at the end of year

$1$ the yield curve will become flat at $9\%.$

$(1)$ Which bond $($and why$)$ should you buy if you plan to close out your position in one

year right after receiving the coupon payment?

$(2)$ Suppose that you can either invest in a two$-$year bond described above, or invest in

a $1-$year bank deposit with an annual interest rate of $6\%.$ As in $($a$),$ your investment

horizon is $1$ year. Which option would you choose and why?