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24 December, 23:38

How long does it take for an investment to double in value if it is invested at 9 % compounded quarterly? Compounded continuously?

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  1. 25 December, 01:36
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    Compounded Quarterly

    We will calculate $100 growing to $200

    Years = log (total/principal) / n*log (1 + rate/n)

    For quarterly compounding n = 4

    Years = log (200 / 100) / 4 * log (1 +.09/4)

    Years = log (2) / 4 * log (1.0225)

    Years = 0.30102999566 / (4 * 0.0096633166794)

    Years = 0.30102999566 / 0.0386532667

    Years = 7.7879574318

    Compounded Continuously

    We will calculate $100 growing to $200

    Years = natural log (total/principal) / rate

    Years = natural log (200 / 100) /.09

    Years = natural log (2) /.09

    Years = 0.69314718056 /.09

    Years = 7.7016353396
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