You manage a bond portfolio, and you are considering an investment in three bonds newly issued by Company X$.$

Bond A has a $10-$year maturity and a call provision: the issuer has the option of redeeming it in full for a price of $100$ at $5$ years to maturity. Bond B pays a coupon of $3\%$ and has $5$ years to maturity with no call provision; Bond C has a coupon of $3\mathrm{.}7\%$ and $10$ years to maturity. Details of the bonds are summarized in the table below:

Assuming there is no change in credit condition and all bonds pay coupons annually.

a$)$ For a $5-$year investment horizon, explain briefly $($without calculation$)$ which of bonds A$,$ B or C will have the highest $($Realized Compound Yield$)$ RCY when the expected interest rates are much lower than now?

b$)$ From $($a$),$ with the scenario that interest rate is lowering in $5$ years$$ time, calculate the $5-$year yield to maturity $($YTM$)$ in order for Bond C to have highest RCY return. You may assume that all the coupons of Bond A$,$ B and C have been reinvested over the first $5$ years at a reinvestment rate of $3\%$ per annum.

c$)$ Assume that Company X has also issued Bond D$,$ with issue price at $100,10$ year maturity and callable in $5$ years at $102.$ Which of the Bonds, A or D will have a longer effective duration, and which of Bonds, A or D will have a higher coupon rate? Briefly explain.v