Calculate the yield to maturity on the following bonds:

a$.$ A $9\mathrm{.}8$ percent coupon $($paid semiannually$)$ bond, with a $$1,000$ face value and $23$ years remaining to maturity. The bond is selling at $$945.$

b$.$ An $10\mathrm{.}3$ percent coupon $($paid quarterly$)$ bond, with a $$1,000$ face value and $10$ years remaining to maturity. The bond is selling at $$905.$

c$.$ An $9\mathrm{.}3$ percent coupon $($paid annually$)$ bond, with a $$1,000$ face value and $10$ years remaining to maturity. The bond is selling at $$1,055.$

Note: For all requirements, do not round intermediate calculations. Round your percentage answers to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161)$

$\backslash$table$[[$a$.$ Yield to maturity,,$\%$ per year$],[$b$.$ Yield to maturity,,$\%$ per year$],[$c$.$ Yield to maturity,,$\%$ per year$]]$