Question

Allison and Leslie, who are twins, just received $50,000 each for their 21th 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 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 20% 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.

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.

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?

Answer 1

Answer:

(a) 208.92years

(b) 188.67years

(c) $6000 ($650 larger than her initial annual contribution)

(d) It is irrational for Allison to invest in the bond fund

Explanation:

Allison and Leslie start annual contribution of $5,000 beginning a year from today (22nd birthday)

(a) Allison starts her investment at 22 in Safety First Bond Fund with returns of 7% per year

Annual total investment = 5000 + (5000 × 0.07) = 5000 + 350 = $5,350

Allison's age when she becomes a millionaire = 22 + (1,000,000/5,350) = (117,700 + 1,000,000)/5,350 = 1,117,700/5,350 = 208.92years

(b) Leslie starts her investment at 22 in New Issue Bio-Tech Fund with returns of 20% per year

Annual total investment = 5000 + (5000 × 0.2) = 5000 + 1000 = $6,000

Leslie's age when she becomes a millionaire = 22 + (1,000,000/6,000) = (132,000 + 1,000,000)/6,000 = 1,132,000/6,000 = 188.67years

(c) Allison's age when she becomes a millionaire is 208.92years

Her annual contributions to become a millionaire at the same age as Leslie = 1,000,000/(188.67 - 22) = 1,000,000/166.67 = $6,000

(d) It is irrational for Allison to invest in the bond fund rather than in stock because it will take longer time to achieve her aspiration to become a millionaire