document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176170>Question 1176170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If $ 500 is decompressed in an account paying 8.5% annual interest, compounded semiannually, how long willit take for the account to increase to $ 1000? How long will it take for the account to increase to $ 41000 if compounded continuously? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #802439 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=802439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not sure what \"decompressed\" means here so will just ignore it<BR>\n" );
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document.write( "If $ 500 in an account paying 8.5% annual interest, compounded semiannually, how long will it take for the account to increase to $ 1000?<BR>\n" );
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document.write( "Using the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%281%2B%28r%2Fn%29%29%5E%28tn%29 ALIGN=MIDDLE  ALT=\"A+=+P%281%2B%28r%2Fn%29%29%5E%28tn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where:<BR>\n" );
document.write( "A = resulting amt after t time<BR>\n" );
document.write( "P = initial amt<BR>\n" );
document.write( "r = interest rate in decimal form<BR>\n" );
document.write( "n = no. of compounding times per yr<BR>\n" );
document.write( "t = no. of yrs<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500%281%2B%28.085%2F2%29%29%5E%282t%29+=+1000 ALIGN=MIDDLE  ALT=\"500%281%2B%28.085%2F2%29%29%5E%282t%29+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify, divide both sides by 500<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B%28.085%2F2%29%29%5E%282t%29+=+2 ALIGN=MIDDLE  ALT=\"%281%2B%28.085%2F2%29%29%5E%282t%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.0425%29%5E%282t%29+=+2 ALIGN=MIDDLE  ALT=\"%281.0425%29%5E%282t%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using natural logs<BR>\n" );
document.write( "2t*ln(1.0425) = ln(2)<BR>\n" );
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document.write( "2t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29%2Fln%281.0425%29 ALIGN=MIDDLE  ALT=\"ln%282%29%2Fln%281.0425%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using your calc<BR>\n" );
document.write( "2t = 16.6535<BR>\n" );
document.write( "divide by 2<BR>\n" );
document.write( "t = 8.327 ~ 8.5 yrs to reach $1000 in the account<BR>\n" );
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document.write( " How long will it take for the account to increase to $ 41000 if compounded continuously?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500%281%2B%28.085%2F2%29%29%5E%282t%29+=+41000 ALIGN=MIDDLE  ALT=\"500%281%2B%28.085%2F2%29%29%5E%282t%29+=+41000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify, divide both sides by 500<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B%28.085%2F2%29%29%5E%282t%29+=+82 ALIGN=MIDDLE  ALT=\"%281%2B%28.085%2F2%29%29%5E%282t%29+=+82\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.0425%29%5E%282t%29+=+82 ALIGN=MIDDLE  ALT=\"%281.0425%29%5E%282t%29+=+82\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using natural logs<BR>\n" );
document.write( "2t*ln(1.0425) = ln(82)<BR>\n" );
document.write( "2t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2882%29%2Fln%281.0425%29 ALIGN=MIDDLE  ALT=\"ln%2882%29%2Fln%281.0425%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using your calc<BR>\n" );
document.write( "2t = 105.8756<BR>\n" );
document.write( "t = 52.938 ~ 53 yrs to reach $41000 in the account\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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