document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054609>Question 1054609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would you solve the questions:\r<BR>\n" );
document.write( "\n" );
document.write( "How long will it take for $1400 dollars to grow to $11,900 at an interest rate of 2.3% if the interested is compounded quarterly?  I am taking the amount and dividing it by the initial investment. My next step has been to plug the following into my TI 84 calculator:\r<BR>\n" );
document.write( "\n" );
document.write( "log(1+.023)8.5\r<BR>\n" );
document.write( "\n" );
document.write( "Can you tell me what I am doing wrong? I get 8.6 years but the correct answer should be 20.65 years. \r<BR>\n" );
document.write( "\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #669805 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=669805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P =initial principal 1,400<BR>\n" );
document.write( "n = number of times the interest is compounded per year (in your case 4)<BR>\n" );
document.write( "F = future amount after time t 11,900<BR>\n" );
document.write( "r = annual nominal interest rate 2.3%<BR>\n" );
document.write( "t = number of years we'll find out<BR>\n" );
document.write( "We need to use the following financial formula:<BR>\n" );
document.write( "t =ln(F/p)/(ln(1+r/n)n)<BR>\n" );
document.write( "t = ln(11,900/1,400)/(ln(1+(0.023/4))4)<BR>\n" );
document.write( "t = (ln 8.5)/((ln 1.00575)*4) do the operations and you'll get 93.31<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "1,400(1+(0.023/4)^4*93.31  =<BR>\n" );
document.write( "1,400(1.00575)^4*93.31<BR>\n" );
document.write( "1,400(1.00575)^373.24 = 11,899.0155<BR>\n" );
document.write( "As you see I lost a few cents in the rounding of the numbers, but the answer is correct.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "John </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );