Assume that the yield curve is YT $=0\mathrm{.}04+0\mathrm{.}001$ T $.$

$($a$)$ What is the price of a par$-$$$1,000$ zero$-$coupon bond with a maturity

of $10$ years?

$($b$)$ Suppose you buy this bond. If $1$year later the yield curve is YT $=0\mathrm{.}042+0\mathrm{.}001$ T $,$ then what will be the net return on the bond?