document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114867>Question 1114867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how long it takes a $3100 investment to earn $500 interest if it is invested at 9% compounded semiannually?<BR>\n" );
document.write( "please can you show me step by step <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 #729807 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula to use is f = p * (1 + r) ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f is the future value.<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your investment is 3100 and you want it to grow to 3100 + 500 = 3600.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your interest rate is 9% per year compounded semi-annually.<BR>\n" );
document.write( "divide 9% by 2 to get 4.5% per semi-annual period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your number of time periods will be in half years, or semi-annual periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your problem, the formula becomes 3600 = 3100 * (1 + .045) ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula uses rate, not percent rate, therefore you need to divide 4.5% by 100 to get a rate of .045 per half year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of that equation by 3100 to get 3600 / 3100 = (1 + .045) ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the log of both sides of that equation to get log(3600 / 3100) = log((1 + .045) ^ n)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since log(1 + .045) ^ n) is equal to n * log(1 + .045), your equation becomes;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(3600 / 3100) = n * log(1 + .045)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of that equation by log(1 + .045) and solve for n to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = log(3600 / 3100) / log(1 + .045) = 3.397144814.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the number of semi-annual periods you will requirie to earn 500 dollars interest on your investment of 3100.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3100 * (1 + .045) ^ 3.97144814 = 3600.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3600 minus 3100 = 500 interest.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );