document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=764362>Question 764362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what rate of interest compounded annually is required to double and investment in 23 years?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #465391 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=465391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what rate of interest compounded annually is required to double and investment in 23 years?<BR>\n" );
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document.write( "Compound interest formula: <BR>\n" );
document.write( "A=P(1+i)^n, P=initial investment, i=interest rate per period, n=number of compound periods, A=amount after n periods<BR>\n" );
document.write( "A/P=(1+i)^n<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given problem:<BR>\n" );
document.write( "A/P=2<BR>\n" );
document.write( "i=?<BR>\n" );
document.write( "n=23<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2=(1+i)^23<BR>\n" );
document.write( "take log of both sides<BR>\n" );
document.write( "log2=23log(1+i)<BR>\n" );
document.write( "log(1+i)=log2/23&#8776;0.013088<BR>\n" );
document.write( "convert to exponential form: (base(10) raised to log of number(0.013088)=number(1+i)<BR>\n" );
document.write( "10^(0.013088)=1+i<BR>\n" );
document.write( "1.030595&#8776;1+i<BR>\n" );
document.write( "i&#8776;.0306&#8776;3.06%<BR>\n" );
document.write( "rate of interest compounded annually required to double and investment in 23 years=3.06%<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1+i)^23=(1.0306)^23&#8776;2<BR>\n" );
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