document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100973>Question 1100973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of years it will take for $28,000 to grow to $29,718 at 6% interest compounded quarterly  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715558 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=715558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>The other tutor's answer is not right.  Maybe you can see what her error was....<br><BR>\n" );
document.write( "Her answer doesn't make sense.  The $28000 at 6% interest for just one year without quarterly compounding would be $29680, so with compounding it will be close to the target value.  So the answer should be something close to 1 year.<br><BR>\n" );
document.write( "The annual interest rate is 6%, or .06; the quarterly interest rate is one-fourth of that, or .015.  So we need to solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28000%281.015%29%5En+=+29718 ALIGN=MIDDLE  ALT=\"28000%281.015%29%5En+=+29718\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where n is the number of compounding periods (quarters of a year).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.015%5En+=+29718%2F28000 ALIGN=MIDDLE  ALT=\"1.015%5En+=+29718%2F28000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%281.015%29+=+log%2829718%2F28000%29 ALIGN=MIDDLE  ALT=\"n%2Alog%281.015%29+=+log%2829718%2F28000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+log%2829718%2F28000%29%2Flog%281.015%29+=+4 ALIGN=MIDDLE  ALT=\"n+=+log%2829718%2F28000%29%2Flog%281.015%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So in fact the answer is that the $29718 value will be reached in 1 year with quarterly compounding. </SPAN>\n" );
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