document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22114>Question 22114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long will it take for an investment to reach 4 times its original value if it is invested at 9.3% APR compounded monthly? compounded continuosly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11811 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=11811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Compound interest formula:  A = P(1+r/n)^(nt)<BR>\n" );
document.write( "A is amount you have now; P is amount you invested; r is annual <BR>\n" );
document.write( "interest rate; n is # of times compounded yearly; t is number of years.<BR>\n" );
document.write( "Let \"x\" be the amount invested and compounded monthly.<BR>\n" );
document.write( "Then \"4x\" is the amount you will have if it reaches 4 times it original value.<BR>\n" );
document.write( "So, 4x = x(1+0.093/12)^(12t)<BR>\n" );
document.write( "    4  = (1.00775)^12t<BR>\n" );
document.write( "Take the log of both sides to get the variable out of the exponent.<BR>\n" );
document.write( "log(4) = (12t)(log(1.00775)<BR>\n" );
document.write( "Solve for \"t\":<BR>\n" );
document.write( "  t = (1/12)[log4/log(1.00775)]<BR>\n" );
document.write( "  t = (1/12)(179.57)<BR>\n" );
document.write( "  t = 14.96 years\r<BR>\n" );
document.write( "\n" );
document.write( "If compounded continuously the formula is A = Pe^rt<BR>\n" );
document.write( "In your case 4x = (x)e^(0.093)t<BR>\n" );
document.write( "Take the natural log of both sides after cancelling the \"x's\" to get:<BR>\n" );
document.write( "ln(4) = 0.093t<BR>\n" );
document.write( "t = [ln4]/0.093<BR>\n" );
document.write( "t = 14.91 years\r<BR>\n" );
document.write( "\n" );
document.write( "Cheers,<BR>\n" );
document.write( "stan H. </SPAN>\n" );
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