Question

Question 2 A state lottery makes the following announcement: "Frederick Carbuncle has just won $100 million! We'll pay Frederick $10 million each year for the next 10 years!" a. Has Frederick really won $100 million? Explain b. Many state lotteries allow winners to choose a single payment instead of a series of annual payments. "We'll offer you the present value of your annual payments, Frederick," the lottery commissioner says. "And because we're feeling generous, we'll use a really high interest rate when we calculate how much that prize will be. Congratulations, Fred!" Comment on the generosity of the lottery commissioner.

Answer 1

a)

We know that Frederick is loosing opportunity of earning interest or return on any other possible investment  if he does not get the lump sum payment. After adjusting the opportunity cost, we can say that present worth of annual payments of lottery is less than a lump sum payment of $100 million today.

So, Frederick has won less than $100 million in the real sense.

b)

We know present value of a series of uniform payments of R is given by

PV=R/(1+i)+R/(1+i)²+R/(1+i)³+...+R/(1+r)ⁿ

We can see that PV of uniform series of payments is negatively related to interest rate. It means present value of a series of payment is lower in case interest rate is higher.

Lottery Commissioner is just using a lucrative language for paying a lower present worth of future annual lottery payments. He is not generous towards Frederick, he is generous towards lottery organizers.