A bond that pays interest semiannually has a $7\mathrm{.}5$ percent promised yield and a price of $$1,145.$ Annual interest rates are now projected to increase $50$ basis points $(100$ basis points $=1\%).$ The bond's duration is $6$ years. What is the predicted new bond price after the interest rate change? $($Watch your rounding.$)$

$$1,111\mathrm{.}89$

None of the options presented

$$1,169\mathrm{.}65$

$$1,070\mathrm{.}36$

$$1\mathrm{.}220\mathrm{.}85$