3a. You win a lottery, and there are no other winners. The announced prize is $30 million which is paid in 30 equal installments of $1 million. The first payment is made right now. Each subsequent payment is made at the end of each of the next 29 consecutive years. If you choose, you can take a lump-sum payment now. Suppose that the lottery commission uses a 6% discount rate. What is the value of the lump-sum payment?

3b. A bond is in a risk class that pays 5% per year. The bond pays annual interest of $400 (first interest payment is one year from now) and matures in 10 years at a value of $10,000. What is the price of the bond?

3c. You win $100,000,000 in a lottery. The lottery commission offers you two options: (1) You can take the lump sum $59,506,497 now. (2) You can get $1,505,143 now and get periodic yearly payments that grow at 5% per year for the next 29 years. (That is, in one year you get $1,505,143(1.05), in two years you get $1,505,143(1.05)(1.05), and so on for 29 years.) What is the implicit discount rate the lottery commission is using if you take the lump sum payout of $59,506,497? Solve this problem using the Goal Seek function in Excel.