$($ Investment Management $)($ Finance $)$

Consider the following three bonds. Bond $A$ is a $1-$year zero$-$coupon bond. Bond $B$ is a $3-$year

bond that pays $70$ in coupons every year and its current price in the market is $P_B=930.$ Bond

C is a $3-$year bond that pays $140$ in coupons every year and its current price in the market is

$P_C=1100.$ All three bonds make a principal payment of $1,000$ upon their expiration. Finally,

the one$-$year spot rate is equal to $r_{01}=7\%.$

a$.$ Using the no$-$arbitrage condition, find the fair price for bond A$.$

b$.$ Use the above information to estimate and plot the $3-$year yield curve.