A share of stock pays a constantly growing $($end$-$of$-$the$-$year$)$ dividend.

If the stock sells for $$\frac{88\mathrm{.}31}{?}$ share today, the dividend to be paid in exactly one year $($at $t=1)$ is $$9\mathrm{.}81,$ and the total return required by investors $($in the stock$)$ is $16\%,$ at what price should each share sell in exactly $5$ years $($at $t=5)?$

$($Answer to the nearest $$0\mathrm{.}01)$