Question $7$

A $$1,000$ bond with a coupon rate of $5\mathrm{.}4\%$ paid semi$-$annually has five years to maturity and a yield to maturity of $7\mathrm{.}5\%.$ If interest rates rise and the yield to maturity increases to $7\mathrm{.}8\%,$ what will happen to the price of the bond? Round to the nearest cent.

rise by $$1006$

rise by $$12\mathrm{.}16$

fall by $$11\mathrm{.}58$

fall by $$9\mathrm{.}82$