Beginning at age 30, a self-employed plumber saves $250 per month in a retirement account until he reaches age 65. The account offers 6% interest, compounded monthly. The balance in the account after t years is given by A(t) = 50,000 (1.005^12t - 1).

a. Compute the balance in the account after 5, 15, 25, and 35 years. What is the average rate of change in the value of the account over the intervals [5, 15], [15, 25], and [25, 35]?

b. Suppose the plumber started saving at age 25 instead of age 30. Find the balance at age 65 (after 40 years of investing).

c. Use the derivative dA/dt to explain the surprising result in part (b) and to explain this advice: Start saving for retirement as early as possible.