Atlantis has been planning to develop a new warning system. The installation of the

system costs more than what their budget allows so the mayor decides to issue a $20-$year

bond to finance the project. The bonds have a face value of $$1,000$ and it promises a

coupon rate of $6\mathrm{.}6\%$ which will be paid quarterly to the bond holders.

a$)$ Calculate the price you have to pay to purchase the bond if

i$.$ The Yield to Maturity $($YTM$)$ is $5\mathrm{.}6\%($annually$)$

ii$.$ The Yield to Maturity $($YTM$)$ is $8\mathrm{.}0\%($annually$)$

b$)$ Let's assume you would like to buy $50$ bonds issued by Atlantis with a $20-$year

tenure. If the YTM is $7\mathrm{.}2\%$ and the coupon rate is $6\mathrm{.}6\%,$ calculate how much

more you have to pay when you purchase a bond which makes annual coupon

payments rather than quarterly.

Consider the following three zero$-$coupon $($discount$)$ bonds:

a$)$ Calculate the one$-,$ two$-,$ and three$-$year spot rates.

b$)$ Calculate the forward rate over the second year and the forward rate over the third year.