Assume, for a particular asset, that

           I = $30,000,
        S_n = 22,000 - 2,000_n,
        B_n = 30,000 - 3,000_n,
O & M_n = 3,000(1 + 0.15)^{n -1},

and

t_m = 0.40,

where

         I = asset purchase price,
      S_n = market value at the end of year n,
      B_n = book value at the end of year n,
O&M_n = O&M cost during year n, and
      t_m = marginal tax rate.

(a) Determine the economic service life of the asset if i = 10%.
(b) Determine the economic service life of the asset if i = 25%.
(c) Assuming that i = 0, determine the economic service life mathematically.