Question

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 =

          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 =

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) [ (1.08^3 - 1)/(0.08)]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 at0.75 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) [ (1.08^n - 1)/(0.08) ]
8.5 = (1.08^n - 1)/(0.08) →0.68 = 1.08^n - 1
n =

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