Question

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?

Answer 1

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.