document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176171>Question 1176171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If $500 is deрosited in an ассount paying 8.5% annual interest, compounded semiannually, how long willit take for the асcount to increase to $1000? Нow long will it take for the account to increase to $1000 if compounded continuously?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #802428 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=802428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is the doubling time of money at 8.5%<BR>\n" );
document.write( "Rule of 70 will say a little more than 8 years (70/8.5)<BR>\n" );
document.write( "P=Po(1+(r/t))^nt<BR>\n" );
document.write( "1000=500(1.0425)^nt<BR>\n" );
document.write( "2=1.0425^nt<BR>\n" );
document.write( "ln of both sides<BR>\n" );
document.write( "ln 2=nt ln(1.0425)<BR>\n" );
document.write( "divide both sides by ln 1.0425<BR>\n" );
document.write( "nt=16.65<BR>\n" );
document.write( "n=2<BR>\n" );
document.write( "so t=8.325 years.<BR>\n" );
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document.write( "The second is 2=e^0.085t<BR>\n" );
document.write( "ln both sides<BR>\n" );
document.write( "ln2=0.085 t<BR>\n" );
document.write( "t=8.15 years, consistent with the rule of 70 (which is actually the rule of 69.3, which is the ln 2 multiplied by 100 to work with rates in per cent rather than decimals.) </SPAN>\n" );
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