Problem $4-55$ in your textbook. However, assume that the equipment is not "valueless" at the end of year $10,$ but can be returned for a $$2500$ credit.A firm expects to install smog control equipment on the exhaust of a gasoline engine. The local smog control district has agreed to pay to the firm a lump sum of money to provide for the first cost of the equipment and maintenance during its $10-$year useful life. At the end of $10$ years the equipment, which initially cost $$10,000,$ is valueless. The firm and the smog control district have agreed that the following are reasonable estimates of the end$-$of$-$year maintenance costs:

$\backslash$table$[[$Year $1,2,3,4,5],[$$$75,100,125,150,175],[$Year $6,7,8,9,10],[$$$200,225,250,275,300]]$

Assuming interest at $6\%$ per year, how much should the smog control district pay to the firm now to provide for the first cost of the equipment and its maintenance for $10$ years?