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

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