Boone County Commissioners want to construct a road to provide another access to

Question

Boone County Commissioners want to construct a road to provide another access to a new
development to reduce emergency response time. The cost of the road is $350,000. It is
estimated that it will cost $2500 to maintain the road the first year. Maintenance costs will
increase by $300 each year after the first year. Every 20 years the County will replace the
road with a new, identical system. The County commissioners want to know the Capitalized
Costs of the road system if they can get two (2) percent annual interest on their money.

Explanation / Answer

Initial cost
350,000

Maintance=principal + 300 every year compounded
2500+2800+3100+3400+3700+4000+4300+4600+4900+5200+5500+5800+6100+6400+6700+7000+7300+7600+7900+8200+8500+8800+9100+9400+9700+10000+10300=172,800

Total cost is 350,000+172,800=522,800 every 25 years for a road.

The capitalized cost is 522,800*(1+interest)^time in years
=522,800(1.07)^25=2,837,461.78

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