4-55 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 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

the  amount that should be paid is $11,292

Explanation:

The computation of the amount that should be paid is shown below:

Present worth is

= $10,000 + $75(P/A, 6%, 10) + $25(P/G, 6%, 10)

= $10,000 + $75 × 7.3601 + $25 × 29.6023

= $11,292

Hence, the  amount that should be paid is $11,292

We simply applied the above calculation

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