How much would an investor lose the first year if she purchased a $30-$year zero$-$coupon bond with a $$1,000$ par value and a $8\%$ yield to maturity, only to see market interest rates increase to $11\%$ one year later?

a$.$

$$55\mathrm{.}70$

b$.$

$$50\mathrm{.}89$

c$.$

$$58\mathrm{.}66$

d$.$

$$53\mathrm{.}93$