All bonds in this question are zero$-$coupon bonds with a par value of $$1,000$ and semi$-$annual compounding.

a$.$ Price $=$$$490\mathrm{.}00,$ Maturity $=11$ years. What is the vield to maturity?

b$.$ Maturity $=6$ years, Yield to maturity $=10\mathrm{.}90\%.$ What is the bond's price $($in $ $)?$

c$.$ Price $=$$$490\mathrm{.}00,$ Yield to maturity $=8\mathrm{.}90\%.$ What is the bond's maturity $($in years, rounded to $2$ decimal places$)?$