document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202792>Question 1202792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long will it take a sum of money to double itself if interest 12(1/2)% per annum  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837901 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "12 & 1/2 = 12.5<BR>\n" );
document.write( "12.5% = 0.125 in decimal form\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you're working with simple interest, then,<BR>\n" );
document.write( "A = P*(1+r*t)<BR>\n" );
document.write( "2P = P*(1+0.125*t)<BR>\n" );
document.write( "2 = 1+0.125*t<BR>\n" );
document.write( "1+0.125*t = 2<BR>\n" );
document.write( "0.125*t = 2-1<BR>\n" );
document.write( "0.125*t = 1<BR>\n" );
document.write( "t = 1/0.125<BR>\n" );
document.write( "t = 8<BR>\n" );
document.write( "It will take 8 years for the money to double at 12.5% simple interest.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you're working with compound interest, when the money is compounded annually, then,<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "2P = P*(1+0.125/1)^(1*t)<BR>\n" );
document.write( "2 = (1.125)^t<BR>\n" );
document.write( "log(2) = log( (1.125)^t )<BR>\n" );
document.write( "log(2) = t*log(1.125)<BR>\n" );
document.write( "t = log(2)/log(1.125)<BR>\n" );
document.write( "t = 5.88494919236171<BR>\n" );
document.write( "t = 5.8849<BR>\n" );
document.write( "It will take about 5.8849 years for the money to double at 12.5% compound interest, when the money is compounded annually.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you're working with compound interest, when the money is compounded semi-annually, then,<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "2P = P*(1+0.125/2)^(2*t)<BR>\n" );
document.write( "2 = (1.0625)^(2t)<BR>\n" );
document.write( "log(2) = log( (1.0625)^(2t) )<BR>\n" );
document.write( "log(2) = 2t*log(1.0625)<BR>\n" );
document.write( "t = log(2)/(2*log(1.0625))<BR>\n" );
document.write( "t = 5.71671343912647<BR>\n" );
document.write( "t = 5.7167<BR>\n" );
document.write( "It will take about 5.7167 years for the money to double at 12.5% compound interest, when the money is compounded semi-annually.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'll skip the steps for other cases of n, but you should get these approximate time values.<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >N</TD><TD >T</TD></tr><tr><TD >1</TD><TD >5.8849</TD></tr><tr><TD >2</TD><TD >5.7167</TD></tr><tr><TD >4</TD><TD >5.6314</TD></tr><tr><TD >12</TD><TD >5.5740</TD></tr><tr><TD >365</TD><TD >5.5461</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );