Today, Zachary and Beth each have $$525,000$ in an investment account. No other contributions will be made to their investment accounts. Both have the same goal: They each want their account to reach $$1$ million, at which time each will retire. Zachary has his money invested in risk$-$free securities with an expected annual return of $4\%.$ Beth has her money invested in a stock fund with an expected annual return of $10\%.$ How many years after Beth retires will Zachary retire?

a$.4\mathrm{.}22$

b$.6\mathrm{.}76$

c$.9\mathrm{.}67$

d$.11\mathrm{.}33$

e$.14\mathrm{.}15$