document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=588088>Question 588088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Struggling with this compound interest question. Please help if you can and provide a detailed explanation of how you got the answer.\r<BR>\n" );
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document.write( "Joe invested $6000 on Feb 22nd, 2012 into an account earning 3 ¾%<BR>\n" );
document.write( "compounded monthly. How many days will it take for his investment to earn<BR>\n" );
document.write( "$2000 in interest?<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 #374368 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=374368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Joe invested $6000 on Feb 22nd, 2012 into an account earning 3 ¾%<BR>\n" );
document.write( "compounded monthly. How many days will it take for his investment to earn<BR>\n" );
document.write( "$2000 in interest?<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Compound Interest Formula: A=P(1+r)^n, P=initial investment, r=interest rate per period, n=number of periods, A=amount after n periods.<BR>\n" );
document.write( "For given problem:<BR>\n" );
document.write( "P=6000<BR>\n" );
document.write( "r=.0375/12=.003125<BR>\n" );
document.write( "n=what we are to find (how many monthsI<BR>\n" );
document.write( "A=amount after n-periods=initial investment +interest=6000+2000=8000<BR>\n" );
document.write( "..<BR>\n" );
document.write( "8000=6000(1+.003125)^n<BR>\n" );
document.write( "8000=6000(1.003125)^n<BR>\n" );
document.write( "8000/6000=(1.003125)^n<BR>\n" );
document.write( "4/3=(1.003125)^n<BR>\n" );
document.write( "take log of both sides:<BR>\n" );
document.write( "log(4/3)=nlog(1.003125)<BR>\n" );
document.write( "n=log(4/3)/log(1.003125)<BR>\n" );
document.write( "using calculator<BR>\n" );
document.write( "n=&#8776;92 months&#8776;2766 days (assumed 30 days/mo) </SPAN>\n" );
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