Question

REACHING A FINANCIAL GOAL

Allison and Leslie, who are twins, just received $35,000 each for their 26th birthdays. 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 13% per year in the fund's relatively short history.

a. If Allison's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Do not round intermediate calculations. Round your answer to two decimal places.
years

b. If Leslie's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Do not round intermediate calculations. Round your answer to two decimal places.
years

c. 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.
$  

d. 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.

-Select-

Please explain how to solve using financial calculator.

Answer 1

a). Allison:

I/Y = 8; PV = -$35,000; PMT = -$5,000 FV = $1,000,000

⇒N = 31.04 year

Allison will be 25+31.04 = 56.04 years old

b). Leslie:

I/Y = 13; PV = -$35,000; PMT = -$5,000 –FV = $1,000,000

⇒N = 21.67 year

Leslie will be 25+21.67 = 46.67 years old

c). If Allison wants to be a millionaire at the same age as Leslie, i.e. after 21.67 yrs, how large would Erika’s annual contribution have to be

I/Y = 6; PV = -$35,000; FV = $1,000,000; N = 21.67

⇒PMT = -$20,736.85

d). Option "I" is correct.

Allison: Investing in a relatively safe fund (high-quality bonds), which has relatively lower return. This means that she has a good chance to achieve her financial goal, but slowly.

Leslie: investing in a very risky fund (small newly-issued bio-tech stocks), which has high average return. So while she might do quite well and become a millionaire shortly, there is also a good chance that she will lose her entire investment.