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$1$

$12\mathrm{.}73\mathrm{.}413\mathrm{.}68$

$22\mathrm{.}73\mathrm{.}412\mathrm{.}77$

$32\mathrm{.}72\mathrm{.}032\mathrm{.}77$

$42\mathrm{.}72\mathrm{.}031\mathrm{.}52$

Using pathwise valuation, what is the proper price for a $3$ year $5\mathrm{.}19\%$ coupon bond?