$1.$ A $3-$year bond provides a coupon of $8\%$ semiannually and has a cash price

of $104.$ What is the bond$$s yield?

$2.$ A default$-$free coupon bond maturing in one year, that pays a coupon

of $5\mathrm{.}00$ after six months and makes a final payment of $105\mathrm{.}00($the last

coupon and the principal$),$ trades at $104\mathrm{.}00$ today. Moreover, a six$-$month

default$-$free zero$-$coupon bond is traded at $98,$ and pays $100\mathrm{.}00$ at maturity.

Find the price of the one$-$year default$-$free zero$-$coupon bond that pays $100$

at maturity using Replication strategy.

$3.$ The one$-$year default free zero$-$coupon bond with face value $100$ trades at

$98,$ and the four$-$year zero coupon bond with face value $100$ trades at $90.$

Enter the $($annualized$)$ forward rate $($as a number for the period between

one year and four years from today:

$4.$ A $10-$year $8\%$ coupon bond currently sells for $$90.$ A $10-$year $4\%$ coupon

bond currently sells for $$80.$ What is the $10-$year spot interest rate?

$5.$ The risk$-$free rate of interest is $7\%$ per annum with continuous compounding. The current value of an index is $150.$

$($a$)$ What is its $6-$month futures price?

$($b$)$ If the future price is $157,$ devise a abritrage strategy

$($c$)$ If there is a dividend of $5$ dollar paid in $4$ months, what should be

the futures price?