document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255701>Question 255701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joe deposits $1000 in an account that earns 5% annual interest compounded semiannually. find out how long it will take for the initial amount to double </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187947 by </B><A HREF=/tutors/aboutme.mpl?userid=EMStelley><B>EMStelley(208)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EMStelley><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=EMStelley><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=187947\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember that the equation for compound interest is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%281+%2B+r%2Fn%29%5E%28nt%29 ALIGN=MIDDLE  ALT=\"A+=+P%281+%2B+r%2Fn%29%5E%28nt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here, P = 1000, r = 0.05, A = 2000 (initial amount doubled) and n = 2.  So we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000+=+1000%281+%2B+0.05%2F2%29%5E%282t%29 ALIGN=MIDDLE  ALT=\"2000+=+1000%281+%2B+0.05%2F2%29%5E%282t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Dividing both sides by 1000 gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+%281.025%29%5E%282t%29 ALIGN=MIDDLE  ALT=\"2+=+%281.025%29%5E%282t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we take the log of both sides in order to get the exponent down:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29+=+2tlog%281.025%29 ALIGN=MIDDLE  ALT=\"log%282%29+=+2tlog%281.025%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by log(1.025):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29%2Flog%281.025%29+=+2t ALIGN=MIDDLE  ALT=\"log%282%29%2Flog%281.025%29+=+2t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Last, divide both sides by 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29%2F%282log%281.025%29%29+=+t ALIGN=MIDDLE  ALT=\"log%282%29%2F%282log%281.025%29%29+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the calculator we have t = 14.04 years. </SPAN>\n" );
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