197. Retirement account A self-employed software engineer starts saving $300 a month in an index fund that returns 9% annual interest, compounded monthly. The balance in the account after t years is given by A(t)40,000 (1.007512 1). a. How much money will be in her account after 20 years and how fast is her account growing at this point? b. How long will it take until the balance in her account reaches $100,000, and how fast is her account growing at this point