Suppose a local asteroid defense system will yield benefits of $1 billion in 300 years by averting large-scale destruction and loss of life. Write an expression for calculating the present discounted value of these benefits using the following time-declining rate schedule: 3 percent for years 1-50, 2.5 percent for years 51-100, 2 percent for years 101-200, 1 percent for years 201-300.