document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198391>Question 1198391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the time needed to Reach an investment goal if you want to say 5000 before buying your first new car and you have 3000 right now tp invest at 3% interest compound monthley<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831977 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=831977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can use a financial calculator or you can use the following formula.<BR>\n" );
document.write( "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( "r is the interest rate per time period<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "in your problem:<BR>\n" );
document.write( "f = 5000<BR>\n" );
document.write( "p = 3000<BR>\n" );
document.write( "r = .03/12<BR>\n" );
document.write( "n = number of months.\r<BR>\n" );
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document.write( "formula becomes:<BR>\n" );
document.write( "5000 = 3000 * (1 + .03/12) ^ n<BR>\n" );
document.write( "divide both sides of the equation by 3000 to get 5/3 = (1 + .03/12) ^ n<BR>\n" );
document.write( "simplify to get 5/3 = 1.0025 ^  n<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(5/3) = log(1.0025^n) which becomes:<BR>\n" );
document.write( "log(5/3) = n * log(1.0025)<BR>\n" );
document.write( "divide both sides of the equation by log(1.0025) to get:<BR>\n" );
document.write( "log(5/3) / log(1.0025) = n<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = 204.585556.<BR>\n" );
document.write( "confirm by replacing n with that and solving for f in the original equation to get:<BR>\n" );
document.write( "f = 3000 * (1 + .03/12) ^ 204.585556 = 5000\r<BR>\n" );
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document.write( "the 3000 will grow to 5000 in 204.585556 months = 17.04879634 years.\r<BR>\n" );
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document.write( "if you used a calculator such as the one at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>, you would get n = 204.59.<BR>\n" );
document.write( "that's the same answer as from the formula, except rounded to 2 decimal places.\r<BR>\n" );
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document.write( "here are the results from using that calculator.\r<BR>\n" );
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document.write( "since the interest rate is compounded monthly, then you need to get the monthly interest rate and you are solving for the number of months. </SPAN>\n" );
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