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?

QUESTION POSTED AT 29/05/2020 - 12:21 AM

Answered by admin AT 29/05/2020 - 12:21 AM

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=future amount
p=initial amount
r=rate and n=time;
thus substituting our values in the expression we have:
introducing the natural logs we get:
n=(ln 1.31)/(ln 1.1)
Therefore is will take 2.8 years for oil to cost more than diesel per gallon.
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