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.