Math
posted by Kate .
You invest $25 in an account earning 7.5% interest per year. After how many years is it worth $42.50?

The general formula for compound interest is:
F=P*(1+i)^n
i=interest per annum, 0.075
n=number of years
F=42.50
P=25
42.5=25(1.075)^n
(1.075)^n=42.5/25=1.7
take log on both sides,
nlog(1.075)=log(1.7)
n=log(1.7)/log(1.075)=7.337 years 
That can't be right...the correct answer shows it should be 12 years.

Please check your figures and your answers.
My answer, figured the long way, is similar to MathMate's. 
I have already applied a quick check using the rule of 72, which states that money doubles every 72/i% years.
In this case, the number of years to double is 72/7.5=9.6 years approximately. So 12 years cannot be right unless there is a typo somewhere.
Are you sure the interest rate is not 4.5% compounded annually?