A 24-year-old December 2012 graduate wants the equivalent of \($2,500,000\) in January 1, 2013, buying power to be available exactly 40 years later on January 1, 2053. He plans to make his first investment of \($Z\) on January 1, 2014, and every year thereafter, with the last payment of \($Z\) on January 1, 2053. He can earn 8 percent on his money and expects inflation to run 5 percent.

a. How many actual dollars will there be in his account immediately after his last deposit?

b. What is \($Z?\)