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 ( <span><span><span>1.0225
</span>
)</span>
</span>Years = 0.30102999566 / (4 * 0.0096633166794)
Years = 0.30102999566 /
<span>
<span>
<span>
0.0386532667
</span>
</span>
</span>
Years =
<span>
<span>
<span>
7.7879574318
</span>
</span>
</span>
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 =
<span>
<span>
<span>
7.7016353396
</span>
</span>
</span>