document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179805>Question 1179805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have $25,000 and I want to have $36,000. If the bank is paying 4.18% compounded monthly, how<BR>\n" );
document.write( "long will it take to reach my goal? (Rounded to the nearest day) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809414 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=809414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula to use is:\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods..\r<BR>\n" );
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document.write( "the interest rate per year = 4.18%<BR>\n" );
document.write( "divide that by 100 to get an interest rate of .0418 per year.<BR>\n" );
document.write( "divide that by 12 to get an interect rate of .0418/12 per month.\r<BR>\n" );
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document.write( "f = 36<BR>\n" );
document.write( "p = 25\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "36 = 25 * (1 + .0418/12) ^ n\r<BR>\n" );
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document.write( "divide both sides by 36 to get:\r<BR>\n" );
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document.write( "36/25 = (1 + .0418/12) ^ n\r<BR>\n" );
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document.write( "take the log of both sides to get:\r<BR>\n" );
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document.write( "log(36/25) = log((1 + .0418/12) ^ n)\r<BR>\n" );
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document.write( "since log(x^n) = n * log(x), this becomes:\r<BR>\n" );
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document.write( "log(36/25) = n * log(1 + .0418/12)\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = log(36/25) / log(1 + .0418/12) = 104.8644495.\r<BR>\n" );
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document.write( "that's the number of months for 25000 to grow to 36000 at 4.18% per year compounded monthly.\r<BR>\n" );
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document.write( "confirm by solving for f with that value of n to get:\r<BR>\n" );
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document.write( "f = 25000 * (1 + .0418/12) ^ 104.8644495 = 36000.\r<BR>\n" );
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document.write( "answer is confirmed to be correct.\r<BR>\n" );
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document.write( "number of months required is 104.8644495.\r<BR>\n" );
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document.write( "number of years required is that divided by 12 = 8.730704122.\r<BR>\n" );
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document.write( "in order to confrim that to be correct, you need the effective interest rate per year.\r<BR>\n" );
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document.write( "that would be equal to (1 + .0418/12) ^ 12 = 1.04261019 minus 1 = .04261019.\r<BR>\n" );
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document.write( "confirm by replacing n with the number of years and r with the effective interest rate per year to get:\r<BR>\n" );
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document.write( "f = 25000 * (1 + .04261019) ^ 8.738704122 = 36000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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