1.

Your lease calls for payments of $500 at the end of each month for the next 12 months. Now your landlord offers you a new 1-year lease that calls for zero rent for the first 3 months, then rental payments of $700 at the end of each month for the next 9 months. You keep your money in a bank time deposit that pays a nominal annual rate of 12 percent. By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 12%/12 = 1%.)

2.

A baseball player is offered a 5-year contract that pays him the following amounts:

Year 1: $1.2 million

Year 2: 1.6 million

Year 3: 2.0 million

Year 4: 2.4 million

Year 5: 2.8 million

Under the terms of the agreement all payments are made at the end of each year.

Instead of accepting the contract, the baseball player asks his agent to negotiate a contract that has a present value of $1 million more than that which has been offered. Moreover, the player wants to receive his payments in the form of a 5-year annuity. The first payment is at t=0 and the last payment is at t=4. All cash flows are discounted at 6 percent. If the team were to agree to the players terms, what would be the players annual salary (in millions of dollars)?

3.

Today is your 20^th birthday. Your parents just gave you $5,000 that you plan to use to open a stock brokerage account. Your plan is to add $500 to the account each year on your birthday. Your first $500 contribution will come one year from now on your 21^st birthday. Your 45^th and final $500 contribution will occur on your 65^thbirthday. You plan to withdraw $5,000 from the account five years from now on your 25^th birthday to take a trip to Europe. You also anticipate that you will need to withdraw $10,000 from the account 10 years from now on your 30^th birthday to take a trip to Asia. You expect that the account will have an average annual return of 11percent. How much money do you anticipate that you will have in the account on your 65^th birthday, following your final contribution?

4.

Today is Rachels 30^th birthday. Five years ago, Rachel opened a brokerage account when her grandmother gave her $25,000 for her 25^th birthday. Rachel added $2,000 to this account on her 26^th birthday, $3,000 on her 27^th birthday, $4,000 on her 28^th birthday, and $5,000 on her 29^th birthday. Rachels goal is to have $400,000 in the account by her 40^th birthday.

Starting today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 11 contributions, the first one will occur today, and the final contribution will occur on her 40^th birthday. Complicating things somewhat is the fact that Rachel plans to withdraw $20,000 from the account on her 35^thbirthday to finance the down payment on a home. How large does each of these 11 contributions have to be for Rachel to reach her goal? Assume that the account has earned (and will continue to earn) an effective return of 10 percent a year.