document.write( "Question 1153394: How long does it take for an investment to double in value if it is invested at 16​% compounded monthly question mark  Compounded​ continuously? \n" ); document.write( "
Algebra.Com's Answer #775647 by MathLover1(20850)\"\" \"About 
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\n" ); document.write( "Use the formula \"A=P%281%2Br%2Fn%29%5Ert\"\r
\n" ); document.write( "\n" ); document.write( "\"r=16%E2%80%8B\"%=\"0.16\"
\n" ); document.write( "\"n=12\"-compounded monthly\r
\n" ); document.write( "\n" ); document.write( "you want \"A+=+2P\" (double your money)\r
\n" ); document.write( "\n" ); document.write( "\"2P=P%281%2B0.16%2F12%29%5E%280.16t%29\"\r
\n" ); document.write( "\n" ); document.write( "\"2=%281%2B0.13333%29%5E%280.16t%29\"\r
\n" ); document.write( "\n" ); document.write( "\"2=%281.13333%29%5E%280.16t%29\".......use log\r
\n" ); document.write( "\n" ); document.write( "\"log%282%29=log%28%281.13333%29%5E%280.16t%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log%282%29=%280.16t%29log%281.13333%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log%282%29%2F%280.16%2Alog%281.13333%29%29=t\"\r
\n" ); document.write( "\n" ); document.write( "\"t=log%282%29%2F%280.16%2Alog%281.13333%29%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"t=log%282%29%2Flog%281.13333%5E0.16%29\"\r
\n" ); document.write( "\n" ); document.write( "\"t=34.6\" years\r
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\n" ); document.write( "\n" ); document.write( "Compounded​ continuously:\r
\n" ); document.write( "\n" ); document.write( "\"A=P%2Ae%5E%28rt%29\"\r
\n" ); document.write( "\n" ); document.write( "you want \"A+=+2P\", and \"r=16%E2%80%8B\"%=\"0.16\"\r
\n" ); document.write( "\n" ); document.write( "\"2P=P%2Ae%5E%280.16t%29\"\r
\n" ); document.write( "\n" ); document.write( "\"2=e%5E%280.16t%29\".....use natural log\r
\n" ); document.write( "\n" ); document.write( "\"ln%282%29=ln%28e%5E%280.16t%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"ln%282%29=%280.16t%29+ln%28e%29\"\r
\n" ); document.write( "\n" ); document.write( "\"ln%282%29=%280.16t%29+%2A1\"\r
\n" ); document.write( "\n" ); document.write( "\"0.16t=ln%282%29\"\r
\n" ); document.write( "\n" ); document.write( "\"t=ln%282%29%2F0.16\"\r
\n" ); document.write( "\n" ); document.write( "\"t=4.33217\" years\r
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