A zero$-$coupon bond with a face value of $$1,000$ with a $20-$year maturity is selling for $$55\mathrm{.}42?$ What is the annualized yield$-$to$-$maturity on this bond? $($assume semi$-$annual compounding$).$

a$.7\mathrm{.}5\%$

b$.7\mathrm{.}8\%$

c$.12\%$

d$.15\%$

e$.15\mathrm{.}6\%$