Allison and Leslie, who are twins, just received $$35,000$ each for their $26$ th birthday. They both have aspirations to become millionaires. Each plans to make a $$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 $8\%$ 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 $15\%$ 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. $

c$.$ Is it rational or irrational for Allison to invest in the bond fund rather than in stocks?

I. High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Allison is rational or irrational, just that she seems to have less tolerance for risk than Leslie does.

II$.$ High expected returns in the market are almost always accompanied by less risk. We couldn't say whether Allison is rational or irrational, just that she seems to have more tolerance for risk than Leslie does.

III. High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Allison is rational or irrational, just that she seems to have more tolerance for risk than Leslie does.

IV$.$ High expected returns in the market are almost always accompanied by less risk. We couldn't say whether Allison is rational or irrational, just that she seems to have less tolerance for risk than Leslie does.

v$.$ High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Allison is rational or irrational, just that she seems to have about the same tolerance for risk than Leslie does.