Erika and Kitty, who are twins, just received $15,000 each for their 20th birthd
ID: 2641769 • Letter: E
Question
Erika and Kitty, who are twins, just received $15,000 each for their 20th 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. Erika opened an account with the Safety First Bond Fund, a mutual fund that invests in high-quality bonds whose investors have earned 5% per year in the past. Kitty 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.
If Erika's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Round your answer to two decimal places.
________ years
If Kitty's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Round your answer to two decimal places.
________ years
How large would Erika's annual contributions have to be for her to become a millionaire at the same age as Kitty, assuming their expected returns are realized? Round your answer to the nearest cent.
$ ________
Is it rational or irrational for Erika to invest in the bond fund rather than in stocks?
High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Erika is rational or irrational, just that she seems to have less tolerance for risk than Kitty does.
High expected returns in the market are almost always accompanied by less risk. We couldn't say whether Erika is rational or irrational, just that she seems to have more tolerance for risk than Kitty does.
High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Erika is rational or irrational, just that she seems to have more tolerance for risk than Kitty does.
High expected returns in the market are almost always accompanied by less risk. We couldn't say whether Erika is rational or irrational, just that she seems to have less tolerance for risk than Kitty does.
High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Erika is rational or irrational, just that she seems to have about the same tolerance for risk than Kitty does.
_________________
Explanation / Answer
The future value F of such payments that are made on a yearly basis and have their interest compounded (annuities) is given by the following formula.
where P is the yearly payment ($5,000 in this case), r is the annual interest rate, and n is the number of years.
n this case F is given (one million) and we need to solve for the number of years n. The above formula can be written in terms of n as
n = log[(F/P) + (r+1)] / log(r+1) - 1
For Erika
F = P [(1+r)^n+1 - (r+1) / r]Related Questions
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