The $6-$month and $1-$year zero rates are both $5\%$ per annum. For a bond that has a life of $18$ months and pays coupon of $4\%$ per annum $($with semi$-$annual payments and one having just been made$),$ the yield is $5\mathrm{.}2\%$ per annum. What is the bond's price?? What is the $18-$month zero rate? All rates are quoted with semi$-$annual compounding.

A $5-$year bond with a yield of $7\%($continuously compounded$)$ pays an $8\%$ coupon at the end of each year. What is the bond's price? What is the bond's duration? Use the duration to calculate the effect on the bond's price of a $0\mathrm{.}2\%$ decrease in its yield.