document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=445137>Question 445137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is:  The amount of money A accrued at the end of t years when a certain amount, P, is invested at an annual rate r compounded n times per year is given by:  A=P(1+r/n)^nt.  How long will it take for $450 at 5% interest compounded monthly to reach $1000?  (Write your answer to two decimal places.)\r<BR>\n" );
document.write( "\n" );
document.write( "I've set the problem up like this:<BR>\n" );
document.write( "1000=450(1+.05/12)^12(t)<BR>\n" );
document.write( "1000=450(1+0.00417)^12(t)<BR>\n" );
document.write( "1000=450(1.00417)^12(t)<BR>\n" );
document.write( "1000=450(1.0512)^t<BR>\n" );
document.write( "1000=473.04^t\r<BR>\n" );
document.write( "\n" );
document.write( "And that's where I'm stuck.  Assuming my math to that point is accurate (and if it's not, could you please help?), how do I go about the problem from this point?  How do I get t to no longer be an exponent and move on to get the time?  \r<BR>\n" );
document.write( "\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #311037 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=311037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I've set the problem up like this:<BR>\n" );
document.write( "1000=450(1+.05/12)^12(t)<BR>\n" );
document.write( "1000=450(1+0.00417)^12(t)<BR>\n" );
document.write( "1000=450(1.00417)^12(t)<BR>\n" );
document.write( "1000=450(1.0512)^t<BR>\n" );
document.write( "1000=473.04^t<BR>\n" );
document.write( "..<BR>\n" );
document.write( "You are correct up to the third step.<BR>\n" );
document.write( "1000=450(1.00417)^12(t)<BR>\n" );
document.write( "divide both sides by 450<BR>\n" );
document.write( "1000/450=(1.00417)^12(t)<BR>\n" );
document.write( "Take the logarithms of both sides<BR>\n" );
document.write( "log(1000/450)=12t*log(1.00417)<BR>\n" );
document.write( "12t=log(1000/450)/log(1.00417)=191.8876<BR>\n" );
document.write( "t=191.8876/12=15.99 years (ans)\r<BR>\n" );
document.write( "\n" );
document.write( "note: Usually, when the unknown is an exponent logs are required to solve. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );