$3.$ Mary just inherited $$100,000.$ She wants to invest the money today, then retire when her nest egg reaches $$1,000,000,$ without adding any additional funds. If she invests the money in CDs with a return of $7\%$ per year, how many years will she have to continue working? How long will she expect to work if she invests instead in the stock market, with a historical return of $12\mathrm{.}6\%?$