Math

Determine how much time is required for an investment to quadruple if interest is earned at a rate of 7.1% compounded continously.

(no other info is given, and that's why I'm confused...)

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  1. When no other info is given, you can start with an arbitrary amount, say $1000, or simply $1.

    The question reduces to:
    In how many years will $1 grow to $4 if the interest is compounded continuously at 7.1% p.a.

    The accumulation function for interest compounded continuously is
    a(t)=e^(rt)
    where a(t) is the future value of $1 compounded at an interest rate of r for t years. E is the base of natural log, equal to approximately 2.7182818284...

    In the present case,
    we have
    4=e^(0.071t)
    Take natural log on both sides and solve for t:
    t=ln(4)/0.071
    =19.525 years

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