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The amount that he will be charged in a special assessment tax to cover his cost of the sidewalk Is $2000  

Explanation:

We are told that the property is an interior lot, so we'll only consider one of the width of his plot, since the sidewalk can only pass through the front or the back of his property.

The property measures 100' x 500' , that is 100 ft width by 500 ft length

The cost of the sidewalk is $40 per linear ft

The city will pick up 50% of the cost.

For a width of the lot, the cost per linear length will be

100 x $40 = $4000

The city covers 50% of this cost, leaving 50% of the cost to the homeowner.

The homeowner's cost will be 50% of $4000

= 0.5 x $4000 = $2000  

The amount that he will be charged in a special assessment tax to cover his cost of the sidewalk Is $2000