Allison and Leslie, who are twins, just received $$20,000$ each for their $30$ th birthday. They both have aspirations to become millionaires. Each plans to make a $$5,000$

annual contribution to her "early retirement fund" on her birthday, beginning a year from today. Allison opened an account with the Safety First Bond Fund, a mutual fund

that invests in high$-$quality bonds whose investors have earned $7\%$ per year in the past. Leslie invested in the New Issue Bio$-$Tech Fund, which invests in small, newly

issued bio$-$tech stocks and whose investors have earned an average of $16\%$ per year in the fund's relatively short history.

a$.$ If the two women's funds earn the same returns in the future as in the past, how old will each be when she becomes a millionaire? Do not round intermediate

calculations. Round your answers to two decimal places.

Allison:

years

Leslie:

years

b$.$ How large would Allison's annual contributions have to be for her to become a millionaire at the same age as Leslie, assuming their expected returns are realized? Do

not round intermediate calculations. Round your answer to the nearest cent.