Question

Allison and Leslie, who are twins, just received $25,000 each for their 22th 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 16% per year in the fund's relatively short history.

1. 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

2. 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.
   $  

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

   1. 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

Answer 1

a]

Number of years taken for each to become a millionaire is calculated using NPER function in Excel :

rate = rate of return earned

pmt = -5000 (Annual contribution. This is entered with a negative sign because it is a deposit into the account)

pv = -25000 (Amount in account today. This is entered with a negative sign because it is like a deposit into the account today)

fv = 1000000 (Required ending value of account)

b]

Annual contribution is calculated using PMT function in Excel :

rate = 8%

nper = 19.60

pv = -25000

fv = 1000000

PMT is calculated to be $20,165.83

c]

I is the correct option.

Higher returns are accompanied by high risk. Allison has less risk tolerance since she invests in the less risky bond fund