document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189963>Question 189963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help I am really stuck on this problem. Need help Please!!!<BR>\n" );
document.write( "A twenty year old student has won one million dollars in the lottery. Is it possible for him to have ten million dollars when he is forty years old if he invests in a CD that earns 4% compounded continuously?\r<BR>\n" );
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document.write( "If the money is invested into a CD that earns 4% compounded daily, how long will it take the student to have ten million dollars? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142542 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=142542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A twenty year old student has won one million dollars in the lottery. Is it possible for him to have ten million dollars when he is forty years old if he invests in a CD that earns 4% compounded continuously? <BR>\n" );
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document.write( "A(t) = A(0)e^(rt)<BR>\n" );
document.write( "10*10^6 = 10^6*e^(0.04t)<BR>\n" );
document.write( "e^(0.04t) = 10<BR>\n" );
document.write( "Take the natural log to get:<BR>\n" );
document.write( "0.04t = ln10 = 2.3026<BR>\n" );
document.write( "t = 2.3026/(0.04) = 57.56.. years<BR>\n" );
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document.write( "Yes: He will then be 78 years old.<BR>\n" );
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document.write( "If the money is invested into a CD that earns 4% compounded daily, how long will it take the student to have ten million dollars?<BR>\n" );
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document.write( "10*10^6 = 10^6(1 + (0.04/365)^(365t)<BR>\n" );
document.write( "(1 + (0.04/365)^(365t) = 10<BR>\n" );
document.write( "1.000109589^(365t) = 10<BR>\n" );
document.write( "365t*log(1.000109589) = log(10)<BR>\n" );
document.write( "365t = 21012.24024<BR>\n" );
document.write( "t = 57.5677 years<BR>\n" );
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document.write( "He will again be 78 year old<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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