Jeff deposits $100$ at the end of each year for $13$ years into Fund X$.$ Rachel deposits $100$ at the end of each year for $13$ years into Fund Y$.$

Fund $x$ earns an annual effective rate of $15\%$ for the first $5$ years and an annual rate of $6\%$ thereafter. Fund Y earns an annual effective rate of $i.$

At the end of $13$ years, the accumulated value of Fund $x$ equals the accumulated value of Fund Y$.$ Calculate $i.$

A$.6\mathrm{.}4\%$

B$.6\mathrm{.}7\%$

C$.7\mathrm{.}0\%$

D$.7\mathrm{.}4\%$

E$.7\mathrm{.}8\%$