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16 May, 12:00

Oil costs $4 per gallon and diesel costs $5.24 per gallon. if the price of oil rises at 10% a month, and the price of diesel is unchanged, how many months will it take before a gallon of oil costs more than a gallon of diesel?

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  1. 16 May, 14:51
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    Given that the gallon of oil cost $4 and that of diesel costs $5.24, to get the time taken for the gallon of oil to cost more than that of diesel we shall proceed as follows;

    Using the compound interest formula;

    A=p (1+r/100) ^n

    where;

    A=future amount

    p=initial amount

    r=rate and n=time;

    thus substituting our values in the expression we have:

    5.24=4 (1+10/100) ^n

    5.24/4 = (1.1) ^n

    introducing the natural logs we get:

    ln (5.24/4) = nln1.1

    thus;

    n = (ln 1.31) / (ln 1.1)

    n=2.8

    Therefore is will take 2.8 years for oil to cost more than diesel per gallon.
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