Question

Allison and Leslie, who are twins, just received $10,000 each for the 25^th birthday. The both aspire to become millionaires. Each plan 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 investment-grade (AAA rated) bonds whose investors have earned 6% 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 10.8% per year in the fund’s relatively short history.

a. If the tow women’s funds earn the same returns in the future as in the past, how old will each be when she becomes a millionaire?

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?

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

Answer 1

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1) Time to be taken by Allison to become millionaire: = NPER(Rate,PMT,PV,FV)

=NPER(0.06,-5000,-10000,1000000)

= 42.07 years

Time to be taken by Leslie to become millionaire:

=NPER(Rate,PMT,PV,FV)

=NPER(0.108,-5000,-10000,1000000)

= 28.50 years

b) Required annual contribution for Allison:

= -PMT(Rate,Nper,PV,FV)

= -PMT(0.06,25,-10000,1000000)

= $ 17444.45

c) It is rational or irrational for Allison to invest in thebond fund rather than in stocks.

• Allison investing in a relatively safe and high quality bonds, which have relatively lower return @6% per annum. This means that she has a good chance to achieve her financial goal, but slowly.

• Leslie investing in a very risky fund ,which have relatively higher return @10.8% per annum . This means that she has a high return with high risk and compared to Allison, she can earn 1,000,000 within 28.50 years.

• It is more rational for Allison to invest in the bond fund rather than stocks because stocks are higher risk and the bio-tech stock is fairly new and so there is probably not enough information to make a proper decision. So, bonds are preferable options for Allison.