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?
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.
