1. Calculating Future Values - You have $20,000 you want to invest for the next 40 years. You are offered an investment plan that will pay you 7 percent per year for the first 20 years and 11 percent per year for the last 20 years. How much will you have at the end of the 40 years? Does it matter if the investment plan pays you 11 percent per year for the first 20 years and 7 percent per year for the next 20 years? Why or why not?

2. Finding the time necessary until you pay off a loan is simple if you make equal payments each month. However, when paying off credit cards many individuals only make the minimum monthly payment, which is generally 2% to 3% of the balance or $10 whichever is greater. Locate the credit card calculator at www.fincalc.com and work out this exercise:

You currently owe $10,000 on a credit card with a 17% interest rate and a minimum payment of $10 or 2% of your balance.

- How soon will you pay off this debt if you make the minimum payment each month?

- How much total interest will you pay using that method?

- Calculate how soon you would pay off this debt if you paid $100 per monthly payment.

3. Find the retirement calculator at www.moneychimp.com to answer the following questions. Suppose you have $1,500,000 when you retire and want to withdraw an equal amount each year for the next 30 years.

- How much can you withdraw each year if you earn 7%

- What if you can earn 9%?

- What if the market failed and your earnings dropped to -.5%. How long would it take to drain your account if you did nothing about this loss pattern?

4. This is a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals:

- Years until retirement: 30

- Amount to withdraw each year: $90,000

- Years to withdraw in retirement: 20

- Interest rate: 8%

5. Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund.

a. If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement?

b. Suppose your friend just inherited a large sum of money. Rather than making equal annual payments, she decided to make one lump-sum deposit today to cover her retirement needs. What amount does she have to deposit today?

c. Suppose your friend's employer will contribute to the account each year as part of the company's profit-sharing plan. In addition, your friend expects a distribution from a family trust several years from now. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

- Employer's annual contribution: $1,500

- Years until trust fund distribution: 20

- Amount of trust fund distribution: $25,000

4. Time value of money. In our opening case study, why would the Toyota Motor Credit Corporation (TMCC) be willing to accept such a small amount today ($1,163) in exchange for a promise to repay about 9 times that amount ($10,000) in the future (30 years)?

- Would you-why or why not? Outline the considerations you used in making your answer.

- Would your answer depend on who is making the promise to repay? Explain your conclusions.

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