document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188721>Question 1188721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if you deposit Php 8000 into an account paying 7% aanual interest compounded quarterly, how long until is Php 12400 in your account </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819876 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=819876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 7% annual interest compounded quarterly is equal to (7/4)% per quarter.\r<BR>\n" );
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document.write( "(7/4)% = 1.7% each quarter.\r<BR>\n" );
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document.write( "divide that by 100 to get a rate of .0175 and add 1 to it to get a growth rate of 1.0175 per quarter.\r<BR>\n" );
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document.write( "you want to know how long before your money reaches 12400.\r<BR>\n" );
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document.write( "1.55 = 1.0175 ^ x, where x represents the number of quarters.\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "log(1.55) = log(1.0175 ^ x).\r<BR>\n" );
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document.write( "since log(1.0175 ^ x) is equal to x * log(1.0175), this becomes:\r<BR>\n" );
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document.write( "log(1.55) = x * log(1.0175).\r<BR>\n" );
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document.write( "divide both sides of the equation by log(1.0175) to get:\r<BR>\n" );
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document.write( "log(1.55) / log(1.0175) = x\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 25.26163279.\r<BR>\n" );
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document.write( "that's how many quarters of a year it will take.\r<BR>\n" );
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document.write( "divide that by 4 to get:\r<BR>\n" );
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document.write( "x = 6.315408196 years.\r<BR>\n" );
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document.write( "confirm by solving for y = 8000 * 1.0175 ^ 25.26163279 to get:\r<BR>\n" );
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document.write( "y = 12400.\r<BR>\n" );
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document.write( "the equation that i worked from 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( "you were given the rate per year of 7%.<BR>\n" );
document.write( "divide that by 100 to get .07 per year.<BR>\n" );
document.write( "divide that by 4 to get .0175 per quarter.\r<BR>\n" );
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document.write( "your time periods are in quarters of a year.\r<BR>\n" );
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document.write( "the equation became:\r<BR>\n" );
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document.write( "12400 = 8000 * (1 + .0175) ^ n\r<BR>\n" );
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document.write( "divide both sides of the equation by 8000 to get:\r<BR>\n" );
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document.write( "12400 / 8000 = (1 + .0175) ^ n\r<BR>\n" );
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document.write( "take the log of both sides of the equation to get:\r<BR>\n" );
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document.write( "log(12400 / 8000) = log((1 + .0175) ^ n) which becomes:\r<BR>\n" );
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document.write( "log(12400 / 8000) = n * log(1 + .0175).\r<BR>\n" );
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document.write( "divide both sides fo log(1 + .0175) to get:\r<BR>\n" );
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document.write( "log(12400 / 8000) / log(1 + .0175) = n\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = 25.26163279.\r<BR>\n" );
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document.write( "sine the time periods were in quarters of a year, then the solution is 25.26163279 quarters of a year, which, when divided by 4, gives you the number of years.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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