document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119614>Question 1119614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Four years after paying $3400 for shares in a startup company, you sell the shares for $1900 at a loss.  What is the total return in percentage and what was the annual return in percentages? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735233 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=735233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you bought the shares for 3400.<BR>\n" );
document.write( "you sold them for 1900.\r<BR>\n" );
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document.write( "your profit ratio is equal to (s - c) / c\r<BR>\n" );
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document.write( "s is the sale price.<BR>\n" );
document.write( "c is the cost.\r<BR>\n" );
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document.write( "this becomes (1900 - 3400) / 3400 = -.4411764706.\r<BR>\n" );
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document.write( "a negative profit is a positive loss.\r<BR>\n" );
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document.write( "your loss ratio is therefore .4411764706.\r<BR>\n" );
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document.write( "multiply that by 100 and your loss percent = 44.11764706.\r<BR>\n" );
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document.write( "that's your total loss percent.\r<BR>\n" );
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document.write( "to determine the annual loss percent, your would use the following formula.\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n\r<BR>\n" );
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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, in this case years.<BR>\n" );
document.write( "n is the number of time periods, in this case years.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "1900 = 3400 * (1 + r) ^ 4\r<BR>\n" );
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document.write( "divide both sides of this equaton by 3400 to get:\r<BR>\n" );
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document.write( "1900 / 3400 = (1 + r) ^ 4\r<BR>\n" );
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document.write( "take the fourth root of both sides of the equqtion to get:\r<BR>\n" );
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document.write( "(1900 / 3400) ^ (1/4) = 1 + r\r<BR>\n" );
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document.write( "subtract 1 from both sides of this equation to get:\r<BR>\n" );
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document.write( "(1900 / 3400) ^ (1/4) - 1 = r\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = -.135393152.\r<BR>\n" );
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document.write( "that's your profit ratio per year.\r<BR>\n" );
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document.write( "your loss ratio per year is .135393152 per year.\r<BR>\n" );
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document.write( "your loss percent per year is 13.5393152 percent per year.\r<BR>\n" );
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document.write( "youo started with 3400 dollars.\r<BR>\n" );
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document.write( "each year you lost 13.5393152 percent of it.\r<BR>\n" );
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document.write( "your average yearly balance is therefore shown as follows:\r<BR>\n" );
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document.write( "beginning of first year = 3400.                                                                  <BR>\n" );
document.write( "end of first year = 2939.663283<BR>\n" );
document.write( "end of second year = 2541.653005<BR>\n" );
document.write( "end of third year = 2197.530594<BR>\n" );
document.write( "end of fourth year = 1900.\r<BR>\n" );
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document.write( "each year you multiply your balance from the previous year by .135393152 and then subtract that number from it to get the balance for that year.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "3400 * .13539352 = 460.3367168.<BR>\n" );
document.write( "3400 - 460.3367168 = 2939.663283.\r<BR>\n" );
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document.write( "this is the balance at the end of the first year as shown above.\r<BR>\n" );
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document.write( "your solution is therefore:\r<BR>\n" );
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document.write( "the total percent loss is 44.11764706 percent.<BR>\n" );
document.write( "the average percent loss each year is 13.5393152 percent.\r<BR>\n" );
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document.write( "round to the required number of decimal places.\r<BR>\n" );
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document.write( "for example, if you are required to round to 2 decimal places, then your solution is:\r<BR>\n" );
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document.write( "44.12% for total percent loss.<BR>\n" );
document.write( "13.54% for average percent loss each year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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