Posted by **Kate** on Wednesday, July 13, 2011 at 5:55pm.

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

- Math -
**MathMate**, Wednesday, July 13, 2011 at 6:17pm
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

- Math -
**Kate**, Wednesday, July 13, 2011 at 7:09pm
That can't be right...the correct answer shows it should be 12 years.

- Math -
**Ms. Sue**, Wednesday, July 13, 2011 at 7:17pm
Please check your figures and your answers.

My answer, figured the long way, is similar to MathMate's.

- Math -
**MathMate**, Wednesday, July 13, 2011 at 9:56pm
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?

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