$($Term structure and bond price$)$ You are given an incomplete specification of the term

structure, as specified by the spot rates and forward rates noted next. You also know

that the price of a $6-$year bond with coupon rate $10\%$ is $$145\mathrm{.}749$ and the price of a

$6-$year bond with coupon rate $5\%$ is $$100\mathrm{.}315.$ For all bonds, the face value is $$100,$

and the coupons are paid annually. Assuming continuous compounding, find the missing

rates.

$s_1=,s_2=6\mathrm{.}9\%,s_3=7\mathrm{.}5\%,s_4=,s_5=8\mathrm{.}4\%,s_6=$

$f_{1,2}=7\mathrm{.}8\%,f_{2,3}=8\mathrm{.}7\%,f_{5,6}=,f_{1,3}=8\mathrm{.}25\%,f_{2,4}=11\mathrm{.}55\%$

If the forward rates are:

$f1,2=3\mathrm{.}8\%$

$f2,5=4\mathrm{.}8\%$

and the spot rates are:

$51=3\mathrm{.}2\%$

$56=5\mathrm{.}1\%$

What is the forward rate $f(5,6)?$