document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255702>Question 255702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Anne deposits $2500 in an account that earns 7.5% annual interest compounded quarterly. Find out how long it will take for Anne to earn $500 in interest </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187945 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=187945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember that the formula 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%5Ent ALIGN=MIDDLE  ALT=\"A+=+P%281+%2B+r%2Fn%29%5Ent\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In this problem, P = 2500, r = 0.075, n = 4 and t is our unknown.  If Anne earns $500 in interest, then the total amount she has is A = 3000.  So our problem is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000+=+2500%281+%2B+0.075%2F4%29%5E%284t%29 ALIGN=MIDDLE  ALT=\"3000+=+2500%281+%2B+0.075%2F4%29%5E%284t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Our first step is to divide both sides by 2500.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2+=+%281.01875%29%5E%284t%29 ALIGN=MIDDLE  ALT=\"1.2+=+%281.01875%29%5E%284t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we need to get the exponent down since that is where the variable is.  So we take the log of both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281.2%29+=+%284t%29log%281.01875%29 ALIGN=MIDDLE  ALT=\"log%281.2%29+=+%284t%29log%281.01875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we divide both sides by log(1.01875):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281.2%29%2Flog%281.01875%29+=+4t ALIGN=MIDDLE  ALT=\"log%281.2%29%2Flog%281.01875%29+=+4t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And last, we divide both sides by 4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281.2%29%2F%284log%281.01875%29%29+=+t ALIGN=MIDDLE  ALT=\"log%281.2%29%2F%284log%281.01875%29%29+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the calculator, we have that t = 2.45 years. </SPAN>\n" );
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