11. Calculating present values. You have just received notifcation that you have won the 2 million first prize in the centennial lottery. However, the prize will be awarded on your 100th birthday, 80 years from now. What present value of your windfall if the appropiate discount rate is 7.5?

12. Calculating Future values. YOur coin collection contains fifty 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2063, assuming they appreaciate at an annual rate of 4.3 percent?

13. Calculating interest rates and future values. In 1895, the first U.S. Open Golf Championship was held. The winners prize money was $150 . In 2014, the winners check was $1620000. What was the precentage increase per year in the winner's check over this period? If the winner's prize increases at the same rate, what will it be in 2040?

14. Calculating Rate of Return. Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby's sold the Edgar Degas bronze sculpture Petite Danseuse de Quatorze Ans at aunction for a price of $10,311,500. Unfortunely for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his annual rate of return on this sculpture?

15. Calculating Rate of return. The 'Brasher doubloon' which was featured in the plot of Raymond Chandler novel The High Window, was sold at auction in 2014 for $4,582,500. The coin had a face value of $15 when it was first issued in 1787 and had been previously sold for $430,000 in 1979. At what annual rate did the coin appreciate from minting to the 1979 sale?What annual rate did the 1979 buyer earn on his purchase? At what annual rate did the coin appreciate from its minting to the 2014 sale?