# Math

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

• Math -

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 -

That can't be right...the correct answer shows it should be 12 years.

• Math -

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

• Math -

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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