Mike and Emily each have invested $$100,000$ in an investment account. No other contributions

will be made to their investment account. Both have the same goal; they each want their account

to reach $$3,000,000$ at which time each will retire. Mike has his money invested in risk$-$free

securities with an expected return of $12\%$ compounded monthly. Emily has her money invested

in a stock fund with an expected return of $15\%$ compounded quarterly. How many years after

Emily retires will Mike retire? $(6$ marks$)$