document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143333>Question 1143333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A promissory note will pay $59,000 at maturity 21 years from now. If you pay $20,000 for the note now, what rate compounded continuously would you earn? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #764125 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=764125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> continuous compounding formula is f = p * e ^ (r * t)\r<BR>\n" );
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document.write( "f = future value = 59,000<BR>\n" );
document.write( "p = present value = 20,000<BR>\n" );
document.write( "n = 21\r<BR>\n" );
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document.write( "you want to solve for r.\r<BR>\n" );
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document.write( "formula becomes 59,000 = 20,000 * e ^ (r * 21)\r<BR>\n" );
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document.write( "divide both sides of he formula by 20,000 to get 2.95 = e ^ (r * 21)\r<BR>\n" );
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document.write( "take the natural log of both sides of the equation to get ln(2.95) = ln(e ^ (r * 21))\r<BR>\n" );
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document.write( "since ln(e ^ (r * 21) = r * 21 * ln(e) and since ln(e) = 1, the formula becomes:\r<BR>\n" );
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document.write( "ln(2.95) = r * 21\r<BR>\n" );
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document.write( "solve for r to get r = ln(2.95) / 21 = 0.051514532\r<BR>\n" );
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document.write( "confirm by replacing r in the original equation to get:\r<BR>\n" );
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document.write( "59,000 = 20,000 * e ^ 0.051514532 * 21)\r<BR>\n" );
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document.write( "this results in 50,000 = 50,000, confirming the solution is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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