PROBLEM 9
CHAPTER 4
A city engineer knows that she will need $25 million in 3 years to
implement new automated toll booths on a toll road in the city.
Traffic on the road is estimated to be 3 million vehicles per year.
How much per vehicle should the toll be to cover the cost of the
toll booth replacement project in 3 years? Interest is 8%
x = toll per vehicle
A = 3,000,000 vehicles/year
F = $25,000,000
n = 3 years
i = 0.08
$25,000,000 = 3,000,000(x) \left[ \frac{1.08^3 - 1}{0.08} \right]
$25,000,000 = 3,000,000(x)(3.2464)
x = $2.57 per vehicle
PROBLEM 17
CHAPTER 4
The automated toll booth system from problem 9 improves traffic
flow and thus reduces greenhouse emissions in the city. Rather
than wait three years, the city can do it now with a 2% loan.
If the toll is set at $0.75 per vehicle, and the state subsidizes
the project at a rate of $0.25 per vehicle, how many years
will it take for the city to pay off the loan?
P = $25,000,000
i = 0.02
x = $1.00 per vehicle
A = 3,000,000 vehicles per year
n = years?
F = P(1 + 0.02) = $25,500,000
$25,500,000 = 3,000,000($1.00) \left[ \frac{1.08^n - 1}{0.08} \right]
8.5 = \frac{1.08^n - 1}{0.08} \rightarrow 0.68 = 1.08^n - 1
n =
