Maturity $=3$ years

Coupon rate $=8\%$

Face value $=$$$1,000$

$YTM=10\%$

Interest is paid annually and the bond is noncallable.

a$.$ Calculate the bond's Macaulay duration $(10$ points$)($Round "Present value" to $2$ decimal places and "Duration" to $4$ decimal place.$)$

b$.$ Calculate the bond's modified duration $(5$ points$)$

c$.$ Assuming the bond's YTM goes from $10\%$ to $9\mathrm{.}5\%,$ calculate an estimate of the price change without considering convexity $(5$ points$).$

d$.$ Calculate the convexity of the bond. $(10$ points$)$