Ten years ago Sandi made a commitment to accumulate $$500,000$ by investing $$350$ at the beginning of every month for as long as it takes. For the first $10$ years she has been earning $13\%$ compounded semiannually. She is now moving all of her money to a safer investment that will earn $9\mathrm{.}6\%$ compounded monthly. She is continuing to invest the $$350$ per month. How much more time will it take Sandi to reach $$500,000?$

Multiple Choice

a$)8$ years, $5$ months

b$)15$ years, $1$ month

c$)21$ years, $1$ month