document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356135>Question 356135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Recall that a formula bank account earning compound interest is\r<BR>\n" );
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document.write( "A=P(1+r/m)^mt - given \r<BR>\n" );
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document.write( "where A is the amount in the bak account after t years, r is the interest rate, and m is the number of the compounding periods per year. If you put $5000 in an account earning 5% interest compounded quarterly, <BR>\n" );
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document.write( "A) how much money will be in the account after 4 years? <BR>\n" );
document.write( "       I figured this part out... I got $6,099.45. <BR>\n" );
document.write( "B) How long will it take until the account is worth $10,000? <BR>\n" );
document.write( "       I got the equation set up... 10,000=5000(1+.05/4)^4t however not sure what to do next.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254204 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=254204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Good start.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10,000\ =\ 5000\left(1\ +\ \frac{0.05}{4}\right)^{4t}\">\r<BR>\n" );
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document.write( "Divide both sides by 5000 and do the arithmetic inside of the parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(1.0125\right)^{4t}\ =\ 2\">\r<BR>\n" );
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document.write( "Now take the log of both sides.  You can use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \log_{10}\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ln\"> -- Doesn't matter, you get the same answer either way.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(1.0125\right)^{4t}\ =\ \ln(2)\">\r<BR>\n" );
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document.write( "Now use:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n)\ =\ n\log_b(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4t\ln\left(1.0125\right)\ =\ \ln(2)\">\r<BR>\n" );
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document.write( "Then divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 4\ln\left(1.0125\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln(2)}{4\ln\left(1.0125\right)}\">\r<BR>\n" );
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document.write( "Now all you have left is a little calculator work.  Let me know what you got.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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