Question

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%.

Answer 1

Answer:

$1.38

Explanation:

She will spend $25 million in 3 years at 10% interest is a case of Future Value of Annuity.

Therefore,

FV = A*((1+r)^n-1)/r

Where A = 25,000,000

r=10%=0.1

n=3

FV= 25000000*((1+0.1)^3-1)/0.1

FV=25000000*(1.331-1)/0.1

FV=25000000*(0.331/0.1)

FV=25000000*3.31

FV=$82,750,000

So it is estimated that 20million cars passes through the toll per year

Therefore,

Toll per vehicle per year = 82750000/2000000

=$4.14

Toll for the duration of the project

=4.14/3 =$1.38