Instructions: There are two questions with three parts each. For all answers, show your work! Show (1) the formula used, (2) the values used for interest rate and number of periods, and (3) calculate the future value factor (FVF) or present value factor (PVF).
Question 1 - In the show Futurama, main character Fry is frozen in the year 2000 and awakens one thousand years later, in the year 3000. At the moment he is frozen, Fry's savings account had a balance of merely $0.93. Upon awakening a thousand years later, he finds his account has a value of $4.3 billion. Fry's savings account earns annual interest at 2.25%.
Part a: Assume interest is compounded annually. Is the show correct? Has Fry's $0.93 turned into $4.3 billion?
Part b: How much would Fry have in his bank account in the year 3000 if his interest had compounded semiannually? What if it were compounded monthly?
Part c: Assume the inflation rate is 3% during the years 2000 - 3000. What is the discounted present value (in the year 2000) of Fry's bank account balance in the year 3000? Hints: Use the future value you calculated in part a (based on annual compounding). Assume inflation discount compounds annually.
Question 2 - You just won the lottery! The jackpot was advertised as $1.5 billion. However, you discover that the $1.5 billion figure is actually the sum of the annuity payments: 30 annual payments of $50 million made at the end of each year. If you want the money as an immediate lump sum, you will only get $930 million.
Part a: Assume the inflation rate is 2%, compounded annually. What is the present value of the annuity payments, discounted for inflation? Is it greater or less than the lump sum offered?
Part b: At what discount rate does the lump sum offered by lottery officials equal the present value of the annuity payments? An approximation is okay here (within 1%).
Part c: Assume that you won't spend any of your lottery winnings for 30 years, regardless of whether you choose lump sum or annuity. Instead, you plan to invest all of your winnings and earn a 10% annual return. Will the future value (at the end of 30 years) be greater with the lump sum, or the annuity? Hint: Calculate the future value in each case and compare. Assume interest compounds annually.