document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=304916>Question 304916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Venture capital. Henry invested $12,000 in a new<BR>\n" );
document.write( "restaurant. When the restaurant was sold two years<BR>\n" );
document.write( "later, he received $27,000. Find his average annual<BR>\n" );
document.write( "return by solving the equation 12,000(1 + r)^2 = 27,000. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218404 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=218404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Average annual return is given by the equation:\r<BR>\n" );
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document.write( "F = P * (1+r)^n\r<BR>\n" );
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document.write( "F = the future value of the money received<BR>\n" );
document.write( "P = the present value of the money invested<BR>\n" );
document.write( "r = the annual interest rate<BR>\n" );
document.write( "n = the number of years.\r<BR>\n" );
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document.write( "In your problem:\r<BR>\n" );
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document.write( "F = $27,000<BR>\n" );
document.write( "P = $12,000<BR>\n" );
document.write( "n = 2\r<BR>\n" );
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document.write( "Your equation becomes:\r<BR>\n" );
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document.write( "27000 = 12000 * (1+r)^2\r<BR>\n" );
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document.write( "Divide both sides of this equation by 12000 to get:\r<BR>\n" );
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document.write( "27000/12000 = (1+r)^2\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "2.25 = (1+r)^2\r<BR>\n" );
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document.write( "Take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "log(2.25) = log((1+r)^2)\r<BR>\n" );
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document.write( "Since, in general, log(x^y) = y*log(x), then your equation becomes:\r<BR>\n" );
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document.write( "log(2.25) = 2 * log(1+r)\r<BR>\n" );
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document.write( "Divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "log(2.25)/2 = log(1+r)\r<BR>\n" );
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document.write( "Use the LOG function of your calculator to get:\r<BR>\n" );
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document.write( ".352182518 / 2 = log(1+r)\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( ".176091259 = log(1+r)\r<BR>\n" );
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document.write( "Find the number whose log is equal to .176091259 using your calculator to get:\r<BR>\n" );
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document.write( "1+r = 1.5\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( "r = .5\r<BR>\n" );
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document.write( "The annual interest rate is equal to .5 which is 50% per year.\r<BR>\n" );
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document.write( "Substitute in your original equation of 2.25 = (1+r)^2 to get:\r<BR>\n" );
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document.write( "2.25 = (1.5)^2\r<BR>\n" );
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document.write( "Use your calculator to find the result of (1.5)^2 to get:\r<BR>\n" );
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document.write( "2.25 = 2.25 confirming that your answer is good.\r<BR>\n" );
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document.write( "Your answer is that the annual interest rate is equal to 50% per year compounded annually.\r<BR>\n" );
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document.write( "In most hewlett packard calculators, you find the log of a number by entering the number and then hitting the LOG key.\r<BR>\n" );
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document.write( "In most hewlett packard calculators, you find the number whose log is by entering the log and then hitting the 2nd key and then hitting the LOG key.\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "I want the log of 100.\r<BR>\n" );
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document.write( "I enter 100 and then hit the LOG key to get 2.\r<BR>\n" );
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document.write( "I want the number whose log is equal to 2.\r<BR>\n" );
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document.write( "I enter 2 and then hit the 2nd key and then hit the LOG key to get 100.\r<BR>\n" );
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document.write( "If you have a different type of calculator, then follow the instructions given with that calculator.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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