document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=962493>Question 962493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I purchased 100 shares of stock for $23.75 per share. Eight months later I sold the stock at $24.50 per share.<BR>\n" );
document.write( "(a.)What annual rate, using simple interest did I earn on this transaction?<BR>\n" );
document.write( "(b.) What annual rate would I have to earn in a saving account compounded monthly to earn the same money on my investment? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588082 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Profit for 1 share: $24.50 - $23.75 = $0.75\r<BR>\n" );
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document.write( "Profit for 100 shares: 100*($0.75) = $75\r<BR>\n" );
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document.write( "So effectively, you have earned $75 in interest. The initial principal is 100*($23.75) = $2375\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "I = P*r*t\r<BR>\n" );
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document.write( "75 = 2375*r*(8/12) ... note: t is in years, 8/12 years = 8 months\r<BR>\n" );
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document.write( "75 = 1,583.3333*r\r<BR>\n" );
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document.write( "r = 75/1,583.3333\r<BR>\n" );
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document.write( "r = 0.04736\r<BR>\n" );
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document.write( "r = 4.74%\r<BR>\n" );
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document.write( "The interest rate is roughly 4.74%\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "A = P*(1+r/n)^(n*t)\r<BR>\n" );
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document.write( "P + I = P*(1+r/n)^(n*t)\r<BR>\n" );
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document.write( "2375+75 = 2375*(1+r/12)^(12*8/12)\r<BR>\n" );
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document.write( "2450 = 2375*(1+r/12)^8\r<BR>\n" );
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document.write( "2450/2375 = (1+r/12)^8\r<BR>\n" );
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document.write( "1.0315789 = (1+r/12)^8\r<BR>\n" );
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document.write( "1+r/12 = 1.0315789^(1/8)\r<BR>\n" );
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document.write( "1+r/12 = 1.00389\r<BR>\n" );
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document.write( "r/12 = 1.00389 - 1\r<BR>\n" );
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document.write( "r/12 = 0.00389\r<BR>\n" );
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document.write( "r = 12*0.00389\r<BR>\n" );
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document.write( "r = 0.04668\r<BR>\n" );
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document.write( "r = 4.67%\r<BR>\n" );
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document.write( "The interest rate needed is approximately 4.67%\r<BR>\n" );
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