The term structure is flat at $6\%.$ A bond has $10$ years to maturity and coupon rate $8\%.$

Coupon payments are semiannual, par values are $100,$ and interest rates are expressed

as semiannual APRs.

$($a$)$ Compute the bond price.

$($b$)$ Compute the bond$$s Macaulay and modified duration.

$($c$)$ Suppose the term structure moves up by $5$ basis points $(1$ basis point $=0\mathrm{.}01\%),$

still staying flat. What is the bond$$s new price?

$($d$)$ Compute the approximate price change using duration, and compare it to the

actual price change.

$($e$)$ Compute the bond$$s convexity.

$($f$)$ Suppose the term structure moves up to $7\%($still staying flat$).$ What is the bond$$s

new price?

$($g$)$ Compute the approximate price change using duration, and compare it to the

actual price change.

$($h$)$ Compute the approximate price change using duration and convexity. Comment

on the accuracy of the approximation.