$1.$ You are considering to buy a $9\%$ semi$-$annual callable bond with $30-$year until maturity and Face Value$=$$$1000.$ The call date is in $6$ years and the call price is $$1020.(25$ points$)$

a$.$ Calculate the current yield if the price is $905\mathrm{.}353555.(2$ point$)$

b$.$ Calculate the YTM$(\%)$ if bond price today is $905\mathrm{.}35355.(5$ points$)$

c$.$ Calculate the yield$-$to$-$call $(2$ point$)$

d$.$ Calculate the yield to worst $(1$ point$)$

e$.$ You are planning to hold this bond for $3-$years from today. Hence, your investment period is $3$ years. Calculate the bond price $3$ years from today when YTM$=8\%,$ which you will sell the bond at this price. $(5$ points$)$

f$.$ What is future value of coupons at year $3$ if you assume that the annual reinvestment rate$=6\%?(5$ points$)$

g$.$What is the percentage total return? $(1$ points$)$

h$.$What is the total dollar return at h end of year $3?(1$ point$)$

i$.$ What is the interest on interest at the end of $3$ years? $(1$ points$)$

j$.$ What percentage of total dollar return is interest on interest? $(1$ point$)$

k$.$ What percentage of total dollar return is capital gain? $(1$ point$)$