Question

Erika and Kitty, who are twins, have aspirations to become millionaires. Each plans to make a $10,000 annual contribution to her “early retirement fund”, beginning a year from today. Erika plans to open an account with the Safety First Bond Fund, a mutual fund that invests in high-quality bonds whose investors have earned 3 percent per year in the past. Kitty will invest in the New Issue Bio-Tech Fund, which invests in small, newly issued bio-tech stocks and whose investors on average have earned 9 percent per year in the fund’s relatively short history.

a) If the two women’s funds earn the same returns in the future as in the past, how much will each twin have in her account at the end of five years? (Use the step-by-step approach.) (5 points)

b) How long will it take each twin to accumulate $1,000,000? (Use your financial calculator.) (2 points)

c) How large would Erika’s annual contributions need to be for her to become a millionaire in 25 years? (Use your financial calculator.) (1 point)

Answer 1

Ans (a): The accumulated amount in the account of both the twins can be calculated as under:

So, Erika and Kitty will have $53,091.36 and $59,847.11 in their accounts respectively, at the end of 5 years.

Ans (b):

The calculation of the number of years required for each twin to reach 1 million is as under:

So, Erika will take 47 years to accumulate an amount of 1 million dollars.

And Kitty will take 27 years to accumulate an amount of 1 million dollars.

*Please note the same calculations can be done on a financial calculator by using TVM feature and entering the following values:

I/Y = respective rate of return (0.03 or 0.09)

PV = 0

PMT = 10000

FV = 1000000

Compute N.

Ans (c):

The annual contribution of Erika for accumulating 1 million dollars can be calculated as under:

Thus, Erika needs an annual contribution of $28,457 to accumulate 1 million dollars in 25 years.

*Please note the same calculations can be done on a financial calculator by using TVM feature and entering the following values:

N = 25

I/Y = 0.03

PV = 0

FV = 1000000

Compute PMT.