(1. (Present value): Sarah Wiggum would like to make a single investment and have $2.2 million at the time of her retirement in 35 years. She has found a mutual fund that will earn 7 percent annually.

a. How much will Sarah have to invest today?

b. If Sarah earned an annual return of 16 percent, how soon could she then retire?

2. (Solving for I) You are considering investing in a security that will pay you $2,000 in 34 years

a. If the appropriate discount rate is 12 percent, what is the present value of this investment? (round to nearest cent)

b. Assume these investments sell for 670 in return for which your receive $2000 in 34 year what is the rate of return investors earn on this investment if they buy it for $670?

3. (Present value comparison) Much to your surprise, you were selected to appear on the TV show "The Price is Right". As a result of your prowess in identifying how many rolls of toilet paper a typical American family keeps on hand, you win the opportunity to choose one of the following: $1700 today, $8000 in 14 years, or $27000 in 29 years. Assuming that you can earn 16 percent on your money, which should you choose?

If you are offered $8000 in 14 years and you can earn 16 percent on your money, what is the present value of $8,000?

4. (Spread sheet problem) If you invest $760 in a bank where it will earn 8 percent compounded annually, how much will it be worth at the end of 7 years?

At the end of 7 years, your bank account will be worth $___

5. (Spread sheet problem) In 17 years, you would like to have $230,000 to buy a vacation home. If you have only $70,000, at what rate must it be compounded annually for it to grow $230,000 in 17 years?

If you have only $70,000, at what rate must it be compounded annually for it to grow to $230,000 in 17 years.

6. (Calculating an EAR) You have a choice of borrowing money from finance company at 18 percent compounded weekly or borrowing money from a bank at20 percent compounded semiannually, Which alternative is the most attractive?

If you can borrow funds from a finance company at 18 percent compounded weekly, the EAR for the loan is ____%

7. (Future value of an ordinary annuity) You are graduating from college at the end of this semester and after reading the The Business of Life in this chapter, you have decided to invest $5,000 at the end of each year into a Roth IRA for the next 45 years.

a. If you earn 8 percent compounded annually on your investment, how much will you have when you retire in 45 years? round to nearest cents

b. How much will you have if you wait 10 years before beginning to save and only make 35 payments into your retirement account?

8. (Future value of a complex annuity) Springfield mogul Montgomery Burns, age 75, wants to retire at age 100 so he can steal candy from babies full time. Once Mr Burns retires, he wants to withdraw $0.9 billion at the beginning of each year for 8 years from special offshore account that will pay 22 percent annually. In order to fund his retirement, Mr Burns will make 25 equal end-of-year deposits in this same special account that will pay 22 percent annually. How much money will Mr Burns need at age 100, and how large of annual deposit must he make to fund this retirement account?

a. If the retirement account will pay 22 percent annually, how much money will Mr Burns need when he retires $___billion (round to three decimal places)

9. (Present value of annuities and complex cash flow) You are given three investment alternatives to analyze. The cash flows from three investments are as follows:

Investment Alternatives

End of year A B C

1 $15,000 $15,000

2 15,000

3 15,000

4 15,000

5 15,000 $15,000

6 15,000 75,000

7 15,000

8 15,000

9 15,000

10 15,000 15,000

Assume an annual discount rate of 19 percent, find the present value of each investment

a. What is the present value of investment A at an annual discount rate of 19 percents? $___ round to the nearest cent.