Julius buys $100$ shares of Acme stock at $$100$ per share on January $1,$ Year $1.$ At the end of the first year

$($December $31,$ Year $1),$ he buys $100$ more shares at $$120$ per share. At the end of the second year

$($December $31,$ Year $2),$ he buys another $100$ shares for $$135$ per share. The stock pays a dividend of $$2\mathrm{.}00$

per share on December $29$th of each year. Acme is trading at $$169\mathrm{.}80$ as of December $31,$ Year $3.$ What is

the time weighted return for Acme since January $1,$ Year $1$ to today?