How long does it take for an investment to double in value if it is invested at 9 % compounded quarterly? Compounded continuou
sly?
1 answer:
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>
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>
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