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:

Year $12345$

$$75100125150175$

Year $678910$

$$200225250275300$

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?