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Your father is $50$ years old and will retire in $10$ years. He expects to live for $25$ years after he retires, until he is $85.$ He wants a fixed retirement income that has the same purchasing power at

the time he retires as $$55,000$ has today. $($The real value of his retirement income will decline annually after he retires.$)$ His retirement income will begin the day he retires, $10$ years from

today, at which time he will receive $24$ additional annual payments. Annual inflation is expected to be $3\%.$ He currently has $$160,000$ saved, and he expects to earn $8\%$ annually on his

savings. How much must he save during each of the next $10$ years $($end$-$of$-$year deposits$)$ to meet his retirement goal? Do not round intermediate calculations. Round your answer to the

nearest dollar.

Allison and Leslie, who are twins, just received $$25,000$ each for their $28$ th birthday. They both have aspirations to become millionaires. Each plans to make a $$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 $18\%$ 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.

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