The Shamrock Corporation has just issued a $$1,000$ par value zero$-$coupon bond with an $6\mathrm{.}00$ percent yield to maturity, due to mature $13$ years from today. $($Assume semiannual compounding.$)$ a$.$ What is the market price of the bond, rounded to the nearest cent? $$ A

b$.$ If interest rates rise to $10$ percent, what will be the price of the bond in three years, rounded to the nearest cent? $$