Question

Allison and Leslie, who are twins, just received $40,000 each for their 24th 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.

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:  
   Leslie:  

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?

Answer 1

a]

The years taken to reach for the fund to reach $1 million is calculated using NPER function in Excel :

Allison:

rate = 8%

pmt = -5000 (annual payment. This is entered as a negative number because it is a cash outflow)

pv = -40000 (beginning amount in fund. This is entered as a negative number because it is like a cash outflow)

fv = 1000000 (required ending amount in fund)

NPER is calculated to be 30.39. It will take 30.39 years for the fund to reach $1 million

Allison's age then = 24 + 30.39 = 54.39

Leslie:

rate = 15%

pmt = -5000 (annual payment. This is entered as a negative number because it is a cash outflow)

pv = -40000 (beginning amount in fund. This is entered as a negative number because it is like a cash outflow)

fv = 1000000 (required ending amount in fund)

NPER is calculated to be 18.93. It will take 18.93 years for the fund to reach $1 million

Leslie's age then = 24 + 18.93 = 42.93

b]

Annual contribution is calculated using PMT function in Excel :

rate = 8%

nper = 18.93 (number of years taken for Leslie to become a millionaire)

pv = -40000

fv = 1000000

PMT is calculated to be $20,125.64

c]

It is irrational for Allison to invest in the bond fund. This is because her capacity to take risk is high due to her very long investment horizon. She can afford to take more risk to earn a higher return, which will result in her achieving her goal faster.