A city engineer knows that she will need 25 million in 3 years to replace toll booths on a toll road in the city. Traffic on the road is estimated to be 20 million vehicles per year. How much per vehicle should the toll be to cover the cost of the toll booth replacement project? Interest is 10%. (Simplify your analysis by assuming that the toll receipts at the end of each year in a lump sum.)

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Matthias Walls

13 February, 04:04

A city engineer knows that she will need 25 million in 3 years to replace toll booths on a toll road in the city. Traffic on the road is estimated to be 20 million vehicles per year. How much per vehicle should the toll be to cover the cost of the toll booth replacement project? Interest is 10%. (Simplify your analysis by assuming that the toll receipts at the end of each year in a lump sum.)

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Harry Mayer · Answer 1

0.50 per vehicle

Explanation:

Given:

Number of years = 3

Number of vehicles per year = 20 million

Amount required = 25 million

Interest rate = 10% = 0.10

Therefore,

Cost of borrowing = Amount required * Interest rate

= 25 million * 0.1

= 2.5 million

Total Toll Booths Replacement Cost = Amount required + Cost of borrowing

= 25 million + 2.5 million

= 27.5 million.

Amount to Charge Per Year = Total Toll Booths Replacement Cost : Number of Years

Lump Sum Amount to Charge Per Year = 27.5 million : 3

= 9.17 million

Yearly toll per vehicle = Lump Sum Amount to Charge Per Year : Number of Vehicles per year

Yearly toll per vehicle = 9.17 million : 20 million

= 0.46 approximately 0.50

Therefore, the toll should be 0.50 per vehicle.

I wish you the best.