document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314555>Question 314555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am confused to which formula to use to solve the following\r<BR>\n" );
document.write( "\n" );
document.write( "After what time will the interest on a certain sum of money at 10% per annum be half of the intial amount.\r<BR>\n" );
document.write( "\n" );
document.write( "I have the rate at 10% and know that I need to find the principal and know that the initial amount will be half.\r<BR>\n" );
document.write( "\n" );
document.write( "Do I do time / rate?\r<BR>\n" );
document.write( "\n" );
document.write( "0.5 / 0.1 = 5 years?\r<BR>\n" );
document.write( "\n" );
document.write( "Help!!<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224928 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=224928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> After what time will the interest on a certain sum of money at 10% per annum be half of the intial amount. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let P = initial amount<BR>\n" );
document.write( "then<BR>\n" );
document.write( "\"principal plus half the amount\" = P + .5P = P(1 + .5) = 1.5P<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Annual compound interest formula:<BR>\n" );
document.write( "M = P( 1 + i )^t<BR>\n" );
document.write( "where<BR>\n" );
document.write( "M is amount (principal plus interest) after time t<BR>\n" );
document.write( "P is initial amount (principal)<BR>\n" );
document.write( "i is interest<BR>\n" );
document.write( "t is time<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In your case<BR>\n" );
document.write( "M = 1.5P<BR>\n" );
document.write( "P = p<BR>\n" );
document.write( "i = .10<BR>\n" );
document.write( "plugging it in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+M+=+P%28+1+%2B+i+%29%5Et+ ALIGN=MIDDLE  ALT=\"+M+=+P%28+1+%2B+i+%29%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.5P+=+P%28+1+%2B+.10+%29%5Et+ ALIGN=MIDDLE  ALT=\"+1.5P+=+P%28+1+%2B+.10+%29%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.5P+=+P%28+1.10+%29%5Et+ ALIGN=MIDDLE  ALT=\"+1.5P+=+P%28+1.10+%29%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "dividing both sides by P:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.5+=+1.10%5Et+ ALIGN=MIDDLE  ALT=\"+1.5+=+1.10%5Et+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "take the log base 1.10 of both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%281.10%2C1.5%29+=+t+ ALIGN=MIDDLE  ALT=\"+log%281.10%2C1.5%29+=+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using \"change of base\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%281.5%29%2Flog%281.10%29+=+t+ ALIGN=MIDDLE  ALT=\"+log%281.5%29%2Flog%281.10%29+=+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4.25+=+t+ ALIGN=MIDDLE  ALT=\"+4.25+=+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > years<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );