document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992185>Question 992185</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Question: $6734 is deposited into a savings account at 4% interest, compounded monthly. To the nearest year, how long will it take for the account balance to reach $1,000,000?\r<BR>\n" );
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document.write( "The question is multiple choice, but when I work it out my answer fits none of the choices.\r<BR>\n" );
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document.write( "My solution: <BR>\n" );
document.write( "A = P (1 + r/m)^n<BR>\n" );
document.write( "A = 1,000,000<BR>\n" );
document.write( "P = 6,734<BR>\n" );
document.write( "r = 4% = 0.04<BR>\n" );
document.write( "m = 12<BR>\n" );
document.write( "n = 12n\r<BR>\n" );
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document.write( "1,000,000 = 6734 (1 + 0.04/12)^12n\r<BR>\n" );
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document.write( "I divide both sides by 6734 cancelling out the number on the right side leaving me with:\r<BR>\n" );
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document.write( "1,000,000/6734 = (1 + 0.04/12)^12n\r<BR>\n" );
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document.write( "148.500 = (1.003)^12n\r<BR>\n" );
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document.write( "I take the LOG of both sides.\r<BR>\n" );
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document.write( "LOG 148.500 = 12n LOG (1.003)\r<BR>\n" );
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document.write( "I divide both sides by 12 LOG (1.003) isolating n. Leaving me with:\r<BR>\n" );
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document.write( "n = LOG 148.500/12 LOG (1.003)\r<BR>\n" );
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document.write( "n = 139.11\r<BR>\n" );
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document.write( "My answer: Approximately 139 years.\r<BR>\n" );
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document.write( "Am I doing something wrong? I just started learning about LOG. Maybe I'm working the problem out wrong. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611798 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=611798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You are doing the problem correctly, but I suspect you have an arithmetic error.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(1\ +\ \frac{0.04}{12}\right)^{12n}\ =\ 148.5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 12n\log(1.00333)\ =\ \log(148.5)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ n\ =\ \frac{\log(148.5)}{12\log(1.00333)}\">\r<BR>\n" );
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document.write( "Check your calculator work; you should get 125 and change.\r<BR>\n" );
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document.write( "I figured out where you went wrong.  You rounded off too soon when you calculated <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(1\ +\ \frac{0.04}{12}\right)\">\r<BR>\n" );
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document.write( "Using 1.003 in the calculation gives you 139 and change.  Using 1.00333... to as many digits as your calculator will keep gives you 125.22+.  Object lesson:  Never round off until the last step in a multi-step calculation.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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