Article is listed above. IN: Indiana Toll Road failing despite 176 percent toll

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Article is listed above.

IN: Indiana Toll Road failing despite 176 percent toll increase for trucks. Reports out of Indiana suggest that the foreign operators of the Indiana Toll Road will soon be filing for bankruptcy in an attempt to restructure more $6 billion in debt. The announcement comes just eight years into the Indiana Toll Road Concession Co.'s 75-year lease of the roadway and despite a 176 percent toll increase on five-axle trucks... . Prior to the lease, a five-axle truck paid $14 to cross the state. That same truck currently pays $38.70 regardless of whether the toll is paid in cash or through E-ZPass. The lease agreement also contained a "non-compete" clause that prohibits the state of Indiana from fixing up nearby toll-free roads that compete with the Indiana Toll Road for traffic...The effects of the lease will continue to compound over time. According to lease language, the operator of the toll road is guaranteed a 3-percent toll increase per year through the year 2081. That means the current $38.70 toll paid by trucks will project out to more than $280 by the time the lease expires. Land Line Magazine

Explanation / Answer

Part (i)

Initial toll = $14

Final toll after increase = $ 38.70

Net increase in toll amount = $ (38.70 - 14) = $ 24.70

So, % of increase = 100 * (24.70/14) = 176.4

This is how the article arrived at the number 176 percent.

Part (ii)

The article mentions that currenty it has been eight years into the 75 years lease period.

So, remaining time of the lease = (75 - 8) years = 67 years

The toll is guranteed to increase at 3% every year. So, it is getting compunded annually at 3%.

We use the formula for compound interest to calculate the toll in the year 2081.

The formula is Amount = Principal * (1+r)t , where r is tha annual rate of increase and t is time in years.

For our case, Principal is the current toll, which is $ 38.70.

Amount is the toll after 67 years, that is in the year 2081.

Also r = 0.03 and t = 67.

So, the toll in 2081, that is the amount = (38.70)*(1+0.03)67 = $ 280.41

This is 41 cents more than $280.

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