math

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Confused!


So here is the question:
Inflation is currently causing the cost of items to increase by about 2.5% per year. In 2009 a litre of gasoline costs approximately $0.90. What will it cost to fill a 60 litre gas tank 10 years from now. Round your answer to the nearest dollar. Name at least one thing other than inflation that determines the cost to the consumer of any article (not just gasoline).

For the mathematical portion, what would be the correct answer?

A = (0.9(1+0.25)^(10)) (60)

60 = # of litres
earlier portion of equation = cost of gas (per litre)

OR

Is the answer..

math - Wayne, Tuesday, April 2, 2013 at 4:35pm

Today it costs $54 to fill tank. In one year (per cent increase problem):
(x - 54)/54 = .025, so x = $55.35
in the next year:
(x - $55.35)/$55.35 = .025, so x = $56.73
Do this 8 more times, and you will get your answer: $69.12
I used an Excel worksheet to generate the answer. Not sure if there's a formula to solve this or not.
math - Wayne, Tuesday, April 2, 2013 at 4:40pm

There is a formula, called the standard future value formula:
54 * (1 + .025)^10 = future value = $69.12

Thanks,

  • math -

    the price increases exponentially
    that is,
    if it increases 2.5% this year, then next year it will increase 2.5% on the NEW amount

    so if 2009 ----> 90 cents
    10 years later ,
    cost = 90(1.025)^10 = 115.20 cents or $1.152

    so to fill a 60 L tank would cost
    60(1.152) = $69.12 or $69 to the nearest dollar.

    BTW, yesterday I paid $1.223 / L in Ontario, the lowest in many weeks.

  • math -

    They are both the same.
    The problem with the first is that 2.5% = 0.025, not 0.25, which is 25%.

    After all, (0.9)(60)=54

    and that is the only difference between the two answers, aside from the typo.

  • math -

    Wow thanks guys, perfect feedback.

    Much appreciated

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