document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199357>Question 1199357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the time required for an investment of 5000 dollars to grow to 9000 dollars at an interest rate of 7.5 percent per year, compounded quarterly. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833207 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=833207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f = p * (1+r) ^ n<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "(1+r) is the growth factor per time period<BR>\n" );
document.write( "r is the growth 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( "in this problem, you get:<BR>\n" );
document.write( "9000 = 5000 * (1+.075/4) ^ n<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "9000 = 5000 * 1.01875 ^ n<BR>\n" );
document.write( "divide both sides of the equation by 5000 and simplify to get:<BR>\n" );
document.write( "9/5 = 1.01875 ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(9/5) = log(1.01875 ^ n)<BR>\n" );
document.write( "this becomes log(9/5) = n * log(1.01875) by the log rule that says that log(x^n) = n * log(x).<BR>\n" );
document.write( "divide both sides of the equation by log(1.01875) to get:<BR>\n" );
document.write( "log(9/5) /log(1.01875) = n<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = 31.64160555 quarters of a year.<BR>\n" );
document.write( "divide that by 4 to get:<BR>\n" );
document.write( "n = 7.910401388 years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you could have used a calculator such as the one found at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a> to get the same answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the inputs to that calculator were:<BR>\n" );
document.write( "pv = -5000 (negaive because it's money you invested.<BR>\n" );
document.write( "fv = 9000 (positive because it's money you got back in treturn after the investment period).<BR>\n" );
document.write( "np = what you want to find.<BR>\n" );
document.write( "pmt = 0 because there is no payment per time period.<BR>\n" );
document.write( "ir = quarterly interest rate = 7.5 / 4 = 1.875%<BR>\n" );
document.write( "payment mad at the end or the beginning of the time period isn't used because there is no payment per time period.<BR>\n" );
document.write( "you click on np and the calculator tells you the number of time periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here are the results from using that cslculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/122501.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );