Arizona Public Utilities has an outstanding bond with a $$1_{2}000$ par value and a $5\%$ coupon rate $($paid annually$)$ which matures in $2$ years. Market interest rates have fallen to $3\mathrm{.}5\%.$ Calculate the value of the bond. $$1,028\mathrm{.}49$

$($b$)$ Suppose the price of the bond falls. What happens to the bond's Yield to Maturity?

$($c$)$ Recalculate the price $($value$)$ assuming the market interest rate increases to $6\%.$ $$981\mathrm{.}67$

$($d$)$ Suppose the price of the bond rises to $$1,000.$ What is the bond's yield to maturity?

$($e$)$ What is the price of the bond if market interest rates equal $5\%?$