1. What is the present value of a security that promises to pay you $5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk.

2. An investment pays you $100 at the end of each of the next 3 years. The investment will then pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the interest rate earned on the investment is 8 percent, what is its present value? What is its future value?

3. You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year, with the first payment being made a year from today, in a bank account that pays 12 percent interest, compounded annually. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal, and how large will the last deposit be?

4. An individual is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a fixed annual retirement income of $65,156. His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. He currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal?

5. You are serving on a jury. A plaintiff is suing the city for injuries sustained after falling down an uncovered manhole. In the trial, doctors testified that it will be 5 years before the plaintiff is able to return to work. The jury has already decided in favor of the plaintiff, and has decided to grant the plaintiff an award to cover the following items:

a. Recovery of 2 years of back-pay ($34,000 for two years ago, and $36,000 for last year, which ends today). Assume that it is December 31 and that all salary is received at year end. This recovery should include the time value of money.