Part $3,$ Fixed income $(90$ points$)$

Consider a $5-$year US treasury note which is sold at $102\%$ of par $($ $$102$ if the par value is $$100\mathrm{.}00).$ It pays a $5\%$ annual coupon, paid semiannually.

A$.$ What is the yield to maturity of the treasury note? $(20$ points$)$

Procter & Gamble has issued a bond with $8\%$ annual coupon, paid semiannually. The settlement date is $\frac{7}{5}\frac{?}{2024}.$ The bond will mature at $\frac{8}{15}\frac{?}{2035}.$ At maturity it will pay $100$ percent, of par. The bond's coupon accrual calculations follow the $30/360$ convention $($this is option $"0"$ in Excel$).$ Please use the YTM you got in question A as the benchmark yield for the P&G bond.

B$.$ What is the bond's clean price? $(10$ points$)$

C$.$ What is the bond's accrued interest? $(10$ points$)$

D$.$ What is the bond's dirty price? $(10$ points$)$

E$.$ What is the Macaulay duration of this bond? $(10$ points$)$

F$.$ What is the modified duration of this bond? $(10$ points$)$

G$.$ Suppose yields rise by $50$ basis points $(0\mathrm{.}50$ percentage points$).$ Use the modified duration to estimate the percent price change. $(10$ points$)$

H$.$ What is the estimated approximate new price of this bond? $(10$ points$)$