Reaching a financial goal
1) Erika and Kitty, who are twins, just received $35,000 each for their 25th 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 15% 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.
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.
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?
2) You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $500. The loan will have a 12% APR based on end-of-month payments.
What is the most expensive car you could afford if you finance it for 48 months? Round your answer to the nearest cent.
What is the most expensive car you could afford if you finance it for 60 months? Round your answer to the nearest cent.
3) Your client is 20 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $3,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 8% in the future.
If she follows your advice, how much money will she have at 65? Round your answer to the nearest cent.
How much will she have at 70? Round your answer to the nearest cent.
She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? Round your answers to the nearest cent.
Annual withdrawals if she retires at 65 $
Annual withdrawals if she retires at 70 $