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Find the amount of time required to double a dollar investment at 7.72%, if the interest is compounded continuously.

4.49 years
8.98 years
17.96 years

I'm not understanding this, I got 3.9 years when I tried to solve this.

  • PreCalc - ,

    The basic formula for compounding continuously is:
    Lim (1+r/n)^(nt)
    as n→∞
    where t=number of years, and r is the annual interest rate.
    which results in the formula:
    For doubling,
    e^(0.0772t) = 2

    Take natural log on both sides to get:
    0.0772t = ln(2)
    Solve for t.

  • PreCalc - ,

    continuous compounding formula is

    amount = principal(e^(it)) , so

    2 = 1(e^.0772t)
    ln2 = ln (e^.0772t)
    .0772 lne = ln2 , but ln e = 1
    t = ln2/.0772 = 8.98

    how did you get 3.9 ?

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