document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209277>Question 1209277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man makes a deposit of $50,000 into an account that pays an annual interest of 5%. How much money will be in the account after 10 years if:<BR>\n" );
document.write( "I. The interest is compounded continuously <BR>\n" );
document.write( "II. How long will it take for the money to triple itself if interest is compounded continuously? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848006 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=848006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part I\r<BR>\n" );
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document.write( "P = 50000 = deposit amount<BR>\n" );
document.write( "e = special constant 2.718 approximately<BR>\n" );
document.write( "r = 0.05 = decimal form of the interest rate<BR>\n" );
document.write( "t = 10 years\r<BR>\n" );
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document.write( "A = P*e^(r*t)<BR>\n" );
document.write( "A = 50000*e^(0.05*10)<BR>\n" );
document.write( "A = 82436.06353501<BR>\n" );
document.write( "A = <font color=red>82436.06</font>\r<BR>\n" );
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document.write( "Part II\r<BR>\n" );
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document.write( "The man deposits P dollars and wants it to triple to 3P dollars. <BR>\n" );
document.write( "You could use P = 50,000 from earlier, but this also works for any positive real number.\r<BR>\n" );
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document.write( "The r value is the same as before.<BR>\n" );
document.write( "The goal is to solve for variable t.\r<BR>\n" );
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document.write( "A = P*e^(r*t)<BR>\n" );
document.write( "3P = P*e^(0.05*t)<BR>\n" );
document.write( "3 = e^(0.05*t)<BR>\n" );
document.write( "Ln(3) = Ln( e^(0.05*t) )<BR>\n" );
document.write( "Ln(3) = 0.05*t*Ln( e )<BR>\n" );
document.write( "Ln(3) = 0.05*t*1<BR>\n" );
document.write( "Ln(3) = 0.05*t<BR>\n" );
document.write( "t = Ln(3)/0.05<BR>\n" );
document.write( "t = <font color=red>21.972246</font>\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "I.  <font color=red>$82,436.06</font><BR>\n" );
document.write( "II.  <font color=red>21.972246 years approximately</font><BR>\n" );
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