You own a $$1,000$ par zero$-$coupon discount bond that has $5$ years to maturity. You plan on selling the bond in one year and believe that the interest rate next year will have the following probability distribution: a$.$ What is your expected price when you sell the bond? & b$.$ What is the standard deviation of the bond's price?

Probability $($Interest Rate$)$

$\mathrm{.}10(6\mathrm{.}60\%)$

$\mathrm{.}20(6\mathrm{.}75\%)$

$\mathrm{.}40(7\mathrm{.}00\%)$

$\mathrm{.}20(7\mathrm{.}20\%)$

$\mathrm{.}10(7\mathrm{.}45\%)$