The Long Run Capitalized Cost of an Asset That Initially $C _ { 0 }$

Short Answer

The long run capitalized cost of an asset that initially cost $C _ { 0 }$ dollars is given by $C = C _ { 0 } + \int _ { 0 } ^ { \infty } A ( t ) e ^ { - r t } d t$ where A(t) is the annual cost of maintenance and r is the annual rate of interest, compounded continuously. Find the long run capitalized cost, in dollars, in the case where $C _ { 0 } = \$ 5,000,000$ , A(t) = 5, 000(1 + 3t), and r = 0.08.