Question $4$

We know that the $6$ month zero bond price is $$94\mathrm{.}9$; the $1$ year coupon bond price is $$90\mathrm{.}0$ with semi$-$annual coupon rate $4\%$; the $1\mathrm{.}5$ year coupon bond price is $$96\mathrm{.}0$ with semi$-$annual coupon rate $8\%.$ Note that the face value of the bonds are $$100.$

What is the annual $1$ year zero rate? Please work on a continuous compounding base.

$8\mathrm{.}16\%$

$14\mathrm{.}65\%$

$14\mathrm{.}39\%$

$10\mathrm{.}57\%$

$7\mathrm{.}87\%$

$10\mathrm{.}31\%$

$8\mathrm{.}60\%$

$7\mathrm{.}84\%$

$10\mathrm{.}47\%$