A semi$-$annual coupon bond, with face value is $1000,$ has $10$ years to maturity and coupon rate

$5\%.$ The first coupon will be paid in $6$ months. The yield to maturity is $4\%,$ and interest rates are

expressed as semiannual APRs.

$($a$)[2$ points$]$ Calculate the bond price.

$($b$)[4$ points$]$ Calculate the bond$$s Macaulay and modified duration.

$($c$)[6$ points$]$ Calculate the bond$$s convexity. Hint: as we need to express duration in terms of

years not periods, we need to express convexity correspondingly.

$($d$)[3$ points$]$ Suppose the YTM $($semiannual APR$)$ moves up by $0\mathrm{.}05\%,$ still staying flat. What is

the bond$$s new price? What is the actual price change in dollars?

$($e$)[3$ points$]$ Calculate the approximate price change in dollars $($new price $$ old price$),$ using

duration approximation.

$($f$)[4$ points$]$ Calculate the approximate price change in dollars $($new price $$ old price$),$ using

duration$-$convexity approximation