A corporate bond with a $4\mathrm{.}0$ percent coupon has $10$ years left to maturity. It has had a credit rating of BBB and a yield to maturity of $6$ percent. The firm has recently invested in a very profitable new project and the rating agency is upgrading the bonds to $A.$ The new appropriate discount rate will be $5\mathrm{.}5$ percent. What will be the change in the bond's price in dollars? Assume interest payments are paid annually and par value is $$1,000.$ Hint: Estimate the first price, estimate the second price, and take the difference.

$$35\mathrm{.}83$

$$37\mathrm{.}66$

$$34\mathrm{.}14$

$$30\mathrm{.}74$