document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164315>Question 1164315</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long will it take the investment to grow to $ 400,000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788637 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P=Po(1+(r/t))^n<BR>\n" );
document.write( "400000=250000(1+.03)^nt, the nt being the total number of times it is compounded. <BR>\n" );
document.write( "1.6=1.03^nt<BR>\n" );
document.write( "ln both sides<BR>\n" );
document.write( "0.4700=nt ln 1.03<BR>\n" );
document.write( "nt=15.901<BR>\n" );
document.write( "t=3.975 years. After 15 quarters it will not be 400000 but after 16 it will be more than 400000.\r<BR>\n" );
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document.write( "Rough check<BR>\n" );
document.write( "12% of 250000 is 30000<BR>\n" );
document.write( "four years of that without compounding would be 120000 more or 370000<BR>\n" );
document.write( "with compounding, the above answer is reasonable.   </SPAN>\n" );
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