document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161502>Question 1161502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use graphical approximation techniques to answer the question. When would an ordinary annuity consisting of quarterly payments of $ 572.62 at 3 % compounded quarterly be worth more than a principal of $ 6900 invested at 5 % simple​ interest?  it is asking for The annuity would be worth more than the principal in approximately ____ years?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785120 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=785120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> two equations are required.\r<BR>\n" );
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document.write( "the first equation is f = p * (1 + r * n)\r<BR>\n" );
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document.write( "to graph this equation, let y = f and x = n<BR>\n" );
document.write( "when p = 6900 and r = .05/4, the equation for graphing becomes:<BR>\n" );
document.write( "y = 6900 * (1 + .05/4 * x)<BR>\n" );
document.write( "y represents the value of the equation for specific values of x.\r<BR>\n" );
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document.write( "the second equation is:\r<BR>\n" );
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document.write( "FUTURE VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS<BR>\n" );
document.write( "f = (a*((1+r)^n-1))/r<BR>\n" );
document.write( "f is the future value of the annuity.<BR>\n" );
document.write( "a is the annuity.<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( "to graph this equation, let y = f and x = n<BR>\n" );
document.write( "when a = 572.62 and r = .03/4, the equation for graphing becomes:<BR>\n" );
document.write( "y = (572.62 * ((1 + .03/4) ^ x - 1)) / (.03/4)<BR>\n" );
document.write( "graph both equations and look for the intersection of the two equations.<BR>\n" );
document.write( "that's when the value of each is the same.<BR>\n" );
document.write( "since the annuity equation is rising faster than the simple interest equation, then the annuity equation will provide a greater value at all values x greater than at the intersection point.\r<BR>\n" );
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document.write( "your solution is that the annuity would be worth more than the principal after approximately 13.428 quarters.\r<BR>\n" );
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document.write( "since x had to be consistent across both equations, then everything had to be in quarters, rather than years.<BR>\n" );
document.write( "in both equations, x represents quarters of a year.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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