1. What is the present value of the following set of cash flows at an interest rate of 6%; $100 now, $600 three years from now, $500 five years from now, and $300 ten years from now.
2. You win the lottery and are told you won $20 million. You actually won payments of $1 million every year for the next 20 years. If your opportunity cost (discount rate) is 10%, how much would you accept today in exchange for those 20 payments?
3. You are saving for your child's college education. You will need tuition which will be $30,000 each year for four years with the first tuition payment due 18 years from today. How much do you need to deposit today in a bank account that earnings 6% today so that you will have enough money to meet all the tuition payments?
4. Alicia wants to have $1,000,000 twenty-five years from now. To achieve it she plans to deposit equal amount of money each month for twenty-five years starting from next month. She believes the rate of interest she can earn is 8% APR. What should be the amount of her monthly deposit?
5. You decide to buy a car for $11,000. Since you do not have the money, you take a loan from the bank for this amount. You are going to pay monthly payments for 4 years. The bank charges 4.8% APR with monthly compounding.
a) What is your monthly payment?
b) What is the EAR
c) What is the remaining balance of the loan at the end of month 3?
6. You are considering a new kind of lease. The lease requires a down payment of $3,000 (made today) and is followed by 40 monthly payments of $450, however you don't make the first payment until 6 months from today. The day you make the last of the 40 payments the lease forces you to buy the car for $10,000. If you can borrow the money to purchase the car at an APR of 9% with monthly compounding, what price would make you indifferent between buying the car and leasing it?