document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028744>Question 1028744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Harper buys a car in 2007 for $20000. Each year,the car decreases in value by 18%. How much will the car be worth in 2012? round to the nearest cent.\r<BR>\n" );
document.write( "\n" );
document.write( "What's the common ratio?<BR>\n" );
document.write( "I got it as 0.18. Is that correct? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643829 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=643829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> wrong.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "he buys the car for 20,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "each year the car decreases in value by 18%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so next year the value of the car is 20,000 - .18*20,000.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor out the common term of 20,000 and you get 20,000 * (1 - .18\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify this to get 20,000 * .82.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your common factor will be .82.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the car is worth 20,000 in 2007<BR>\n" );
document.write( "you want to know how much the car is worth in 2012.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2012 - 2007 = 5 years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for compound value is f = p * (1+r)^n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your case, p = 20,000.<BR>\n" );
document.write( "r = -.18<BR>\n" );
document.write( "n = 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation becomes f = 20,000 * (1 - .18)^5 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 20,000 * .82^5 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 7,414.796864\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the car will be worth 7,414.796864 in 5 years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can do the yearly calculations and you'll get the same answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with 20,000 in 2007.<BR>\n" );
document.write( "in 2008, the value of the car is 20,000 - .18 * 20,000 = 16,400.<BR>\n" );
document.write( "in 2009, the value of the car is 16,400 - .18 * 16,400 = 13,448.<BR>\n" );
document.write( "in 2010, the value of the car is 13,448 - .18 * 13,448 = 11,027.36<BR>\n" );
document.write( "in 2011, the value of the car is 11,027.36 - .18 * 11,027.36 = 9,042.44.<BR>\n" );
document.write( "in 2012, the value of the car is 9,042.44 - .18 * 9,042.44 = 7414.80.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the same as the answer we got above after rounding to 2 decimal digits.\r<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" );