document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031446>Question 1031446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a sum of 50,000 dollars I have 2 investment options:<BR>\n" );
document.write( "A long term certificate of deposit that pays an annual rate of 4.25% compounded quarterly .<BR>\n" );
document.write( "A mutual fund that over the past several years averaged a return of 5% compounded annually.<BR>\n" );
document.write( "For each investment option how long will it take for me to double my money?<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 #646138 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=646138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P=Po{1+r/t)^nt<BR>\n" );
document.write( "P/Po=2 when it doubles.<BR>\n" );
document.write( "2=(1+0.0425/4)^4n<BR>\n" );
document.write( "ln of both sides <BR>\n" );
document.write( "ln2=4nln(1+(0.0425/4)); divide both sides by ln(1+(0.0425/4))<BR>\n" );
document.write( "=65.58.  Divide that (still not rounded) by 4 to get n in years.<BR>\n" );
document.write( "16.4 years (now round).<BR>\n" );
document.write( "Notice that the 50,000 doesn't even need to appear.  Doubling the money is doubling the money.<BR>\n" );
document.write( "Notice that the rule of 72 would say that doubling would take just under 18 years (for 4%) and 16.94 years for 4.25%.  The answer makes sense.<BR>\n" );
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document.write( "2=(1.05)^n<BR>\n" );
document.write( "ln2= n ln (1.05)<BR>\n" );
document.write( "n=14.2 years.<BR>\n" );
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