Sandy is planning to accumulate $$500,000$ after $30$ years by making investments of $$300$ at the end of each month for $20$ years and leaving the money to grow at $7\%$ compounded semiannually for $10$ more years. What monthly compounded nominal rate will Sandy have to be earning over the $20$ years that she makes the monthly deposits?$08\mathrm{.}96\%11\mathrm{.}30\%7\mathrm{.}12\%12\mathrm{.}83\%10\mathrm{.}75\%$