A five$-$year French government bond $($OAT$)$ makes annual coupon payments of $4\mathrm{.}0\%$ and offers a yield to maturity of $3\mathrm{.}0\%$ annually compounded. The face value is $1000$ euro.

Questions:

a$)$ What is the price of this bond?

b$)$ Now, suppose the bond price has suddenly moved to $1000$ euro. What is the yield to maturity of the bond now?