document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=438977>Question 438977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello:<BR>\n" );
document.write( "I have a problem I cannot seem to solve. I am hoping you can help me solve it or point me in the right direction. I am trying to solve the compound interest formula for the time variable; however my memory of log is very shady. What I need is:\r<BR>\n" );
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document.write( "given a starting dollar amount<BR>\n" );
document.write( "a fixed monthly deposit<BR>\n" );
document.write( "and a fixed interest rate\r<BR>\n" );
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document.write( "I want to know how long until the balance reaches X amount?\r<BR>\n" );
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document.write( "the original formula that solves for final balance is\r<BR>\n" );
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document.write( " B = A(1+i)^N + (P/i)[(1+i)^N &#8722; 1]<BR>\n" );
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document.write( " B = ending balance<BR>\n" );
document.write( " A = starting balance<BR>\n" );
document.write( " i = monthly rate<BR>\n" );
document.write( " P = monthly deposits<BR>\n" );
document.write( " n = how many months\r<BR>\n" );
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document.write( "thanks in advance!\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #303445 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=303445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> B = A(1+i)^N + (P/i)[(1+i)^N &#8722; 1]\r<BR>\n" );
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document.write( "Solve for \"N\":<BR>\n" );
document.write( "A(1+i)^N + (P/i)(1+i)^N = B+1<BR>\n" );
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document.write( "[A + (P/i)](1+i)^N = B+1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(1+i)^N = (B+1)/[A+(P/i)]<BR>\n" );
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document.write( "Take the log of both sides:<BR>\n" );
document.write( "N*log(1+i) = log[(B+1)/((Ai+P)/i)]<BR>\n" );
document.write( "----<BR>\n" );
document.write( "N = {log[(B+1)/((Ai+P)/i)]}/log(1+i)<BR>\n" );
document.write( "=========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "==================<BR>\n" );
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