Following are the one$-$year forward rates stated on the basis of annual compounding:

Time period Forward Rate

$0$y$1$y $4\mathrm{.}410\%$

$1$y$1$y $4\mathrm{.}620\%$

$2$y$1$y $4\mathrm{.}800\%$

$3$y$1$y $4\mathrm{.}880\%$

$4$y$1$y $4\mathrm{.}950\%$

a$.$ b$.$ c$.$ Calculate the implied $4-$year spot rate.

Calculate the price of a $3-$year bond with a par value of $100$ paying a $6\mathrm{.}80\%$ coupon.

What is the yield to maturity of this bond $($using the answer to $($b$)?$