document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854352>Question 854352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much money should Rita invest 6 2/3% stock at 110 to source an annual income of 900? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514621 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=514621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> she buys the stock at 110 per share and it will give her 6 2/3 % interest per year is what i think you are asking.\r<BR>\n" );
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document.write( "6 2/3 % per year is equal to 20/3 % per year which is equal to an interest rate of 20/300 per year.\r<BR>\n" );
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document.write( "if we let x = the number of shares, then the formula becomes:\r<BR>\n" );
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document.write( "20/300 * 110 * x = 900\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "1/15 * 110 * x = 900\r<BR>\n" );
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document.write( "multiply both sides of this equation by 15 to get:\r<BR>\n" );
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document.write( "110 * x = 900 * 15 = 13500\r<BR>\n" );
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document.write( "divide both sides of this equation by 110 to get:\r<BR>\n" );
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document.write( "x = 13500 / 110\r<BR>\n" );
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document.write( "this can be simplified to 1350 / 11 which can't really be simplified any further.\r<BR>\n" );
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document.write( "we'll keep it as a fraction to avoid never ending decimals which have to be rounded.\r<BR>\n" );
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document.write( "the number of shares is equal to 1350 / 11\r<BR>\n" );
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document.write( "let's see if this works.\r<BR>\n" );
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document.write( "formula was 20 / 300 * 110 * x = 900\r<BR>\n" );
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document.write( "we replace x with 1350 / 11 to get:\r<BR>\n" );
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document.write( "20 / 300 * 110 * 1350 / 11 = 900\r<BR>\n" );
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document.write( "simplify the left side of this equation to get 900 = 900\r<BR>\n" );
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document.write( "this is what we were looking for so the solution is good.\r<BR>\n" );
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document.write( "you could also convert everything to decimals and you'll get the same answer or something very close to it depending on whether round intermediate results or not.\r<BR>\n" );
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document.write( "let's start again and work it with decimal equivalents rather than fractions.\r<BR>\n" );
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document.write( "you pay 110 a share.\r<BR>\n" );
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document.write( "x = number of shares.\r<BR>\n" );
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document.write( "interest rate is 6 and 2/3 % which is equivalent to 6.6667 % which is equal to .066667 interest rate.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( ".066667 * 110 * x = 900\r<BR>\n" );
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document.write( "divide both sides of this equation by .066667 * 110 and you get:\r<BR>\n" );
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document.write( "x = 900 / (.066667 * 110) = 122.726659\r<BR>\n" );
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document.write( "122.726659 shares at 110 apiece cost 13499.93249 dollars.\r<BR>\n" );
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document.write( ".066667 * 13499.93249 is equal to 899.9999993\r<BR>\n" );
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document.write( "the answer is very close to 900 and would have been exactly equal to 900 if i didn't round intermediate results.\r<BR>\n" );
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document.write( "since i was pretty liberal with the number of decimal digits i carried it out to, the answer was extremely close.   rounding intermediate results to 1 or 2 decimal digits would have been further away.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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