Math

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

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asked by Kate
  1. 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

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

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    posted by Kate
  3. Please check your figures and your answers.

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

  4. 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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