document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003761>Question 1003761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many years time will a sum of money quintuple at a rate of 4% per annum compounded quarterly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620411 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=620411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general formula 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( "your problem wants to know when your money will quintuple if you invest it at 4% per year compounded quarterly.\r<BR>\n" );
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document.write( "your compounding periods per year are 4.<BR>\n" );
document.write( "your number of time periods will be 4 * the number of years.<BR>\n" );
document.write( "your interest rate per time period will be the annual interest rate divided by 4.\r<BR>\n" );
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document.write( "4% per year give you an interest rate of .04 per year.<BR>\n" );
document.write( "divide that by 4 and you get an interest rate of .01 per time period, with each time period being a quarter of a year.\r<BR>\n" );
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document.write( "you want to quintuple our money, so set f = 5 and p = 1.\r<BR>\n" );
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document.write( "the formula of f = p * (1+r)^n becomes:\r<BR>\n" );
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document.write( "5 = 1 * 1.01^n\r<BR>\n" );
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document.write( "this can be written as 5 = 1.01^n because 1 times anything is equal to anything.\r<BR>\n" );
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document.write( "so you start with 5 = 1.01^n\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get log(5) = log(1.01^n).\r<BR>\n" );
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document.write( "since log(1.01^n) is equivalent to n * log(1.01), your equation becomes:\r<BR>\n" );
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document.write( "log(5) = n * log(1.01)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(1.01) to get:\r<BR>\n" );
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document.write( "log(5) / log(1.01) = n\r<BR>\n" );
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document.write( "use your calculator to solve for n to get:\r<BR>\n" );
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document.write( "n = 161.7471757\r<BR>\n" );
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document.write( "since your time period is in quarters of a year, you need to divide that by 4 to get the number of years.\r<BR>\n" );
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document.write( "your solution is that the number of years for your money to quintuple is 40.43679392 years.\r<BR>\n" );
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document.write( "to prove this is correct, go back to your formula and replace n with 4 * 40.43679392 to get 161.7471757 and your equation will become:\r<BR>\n" );
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document.write( "5 = 1 * 1.01^161.7471757\r<BR>\n" );
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document.write( "solve this equation to get 5 = 5\r<BR>\n" );
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document.write( "this confirms the equation is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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