document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192786>Question 1192786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you invest $600 into an account that compounds continuously at a rate of 1.75%. How long would you have to leave the money in the account to have an ending balance of $1350? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824682 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula for continuous compounding is:<BR>\n" );
document.write( "f = p * e ^ (r * n)<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the rate per time period<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "your time periods are in years.<BR>\n" );
document.write( "with p = 600 and f = 1350 and r = .0175, the formula becomes:<BR>\n" );
document.write( "1350 = 600 * e ^ ( .0175 * n)<BR>\n" );
document.write( "note that the decimal equivalent of the rate is used, not the percent.<BR>\n" );
document.write( "decimal equivalent of rate = percent / 100.<BR>\n" );
document.write( "1.75% = .0175.\r<BR>\n" );
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document.write( "divide both sides of 1350 = 600 * e ^ ( .0175 * n) by 600 to get:<BR>\n" );
document.write( "2.25 = e ^ (.0175 * n)<BR>\n" );
document.write( "take the natural log of both sides of this equation to get:<BR>\n" );
document.write( "ln(2.25) = .n(e ^ (.0175 * n)<BR>\n" );
document.write( "because ln(e^x) = x*ln(e) and ln(e) = 1, the equation becomes:<BR>\n" );
document.write( "ln(2.25) = .0175 * n<BR>\n" );
document.write( "divide both sides of this equation by .0175 and solve for n to get:<BR>\n" );
document.write( "n = ln(2.25) / .0175 = 46.3388695.<BR>\n" );
document.write( "confirm by replacing n in the equation with that to get:<BR>\n" );
document.write( "f = 600 * e ^ (.0175 * 46.3388695) = 1350.<BR>\n" );
document.write( "this confirms the value of n is good.\r<BR>\n" );
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document.write( "your solution is that you would have to leave the money in the account for 46.3388695 years to allow it to grow to 1350 at 1.75% per year compounded continuously.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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