I already have the solution but I want you to explain with details why we use ( A F i% n) versus (A P i% n) ?

A municipality is planning on constructing a water treatment plant at an initial cost of $10,000,000. Every 5 years, major repairs and cleanup are required at a cost of $2,000,000. Due to the necessity to remove sludge and make minor repairs, annual costs of operating the treatment plant are estimated to be $700,000, $775,000, $850,000, $925,000, and $1,000,000 each year leading up to the 5-year major repair and cleanup. Based on a 4 percent/year TVOM, what is the capitalized cost for the water treatment plant? A municipality is planning on constructing a water treatment plant at an initial cost of $10,000,000. Every 5 years, major repairs and cleanup are required at a cost of $2,000,000. Due to the necessity to remove sludge and make minor repairs, annual costs of operating the treatment plant are estimated to be $700,000, $775,000, $850,000, $925,000, and $1,000,000 each year leading up to the 5-year major repair and cleanup. Based on a 4 percent/year TVOM, what is the capitalized cost for the water treatment plant