After building a binomial interest rate tree, you have identified the following possible interest rate paths:

Path y$0$y$1$ y$1$y$1$ y$2$y$1$

$12\mathrm{.}553\mathrm{.}383\mathrm{.}76$

$22\mathrm{.}553\mathrm{.}382\mathrm{.}72$

$32\mathrm{.}552\mathrm{.}042\mathrm{.}72$

$42\mathrm{.}552\mathrm{.}041\mathrm{.}6$

Using pathwise valuation, what is the proper price for a $3$ year $6\mathrm{.}59\%$ coupon bond?