document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120055>Question 1120055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use graphical approximation techniques or an equation solver to approximate the desired interest rate. A person makes annual payments of $ 1000 into an ordinary annuity. At the end of 5 &#8203;years, the amount in the annuity is $ 5703.88. What annual nominal compounding rate has this annuity&#8203; earned? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735729 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=735729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person makes annual payments of $ 1000 into an ordinary annuity.<BR>\n" );
document.write( " At the end of 5 years, the amount in the annuity is $ 5703.88.<BR>\n" );
document.write( " What annual nominal compounding rate has this annuity earned?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can use the annuity formula<BR>\n" );
document.write( "P(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Bi%29%5Et-1%29%2Fi ALIGN=MIDDLE  ALT=\"%28%281%2Bi%29%5Et-1%29%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = Fv; where<BR>\n" );
document.write( "P =payment<BR>\n" );
document.write( "i = interest rate<BR>\n" );
document.write( "t = periods<BR>\n" );
document.write( "Fv = Final value<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1000(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Bi%29%5E5-1%29%2Fi ALIGN=MIDDLE  ALT=\"%28%281%2Bi%29%5E5-1%29%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = 5703.88<BR>\n" );
document.write( "Put in the form that we can graph; i = x<BR>\n" );
document.write( "1000(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Bx%29%5E5-1%29%2Fx ALIGN=MIDDLE  ALT=\"%28%281%2Bx%29%5E5-1%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = 5703.88<BR>\n" );
document.write( "divide both sides by 1000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Bx%29%5E5-1%29%2Fx ALIGN=MIDDLE  ALT=\"%28%281%2Bx%29%5E5-1%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5703.88%2F1000 ALIGN=MIDDLE  ALT=\"5703.88%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Approx solution; x = .066 or 6.6% interest<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Bx%29%5E5-1%29%2Fx ALIGN=MIDDLE  ALT=\"%28%281%2Bx%29%5E5-1%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5.704<BR>\n" );
document.write( "multiply both sides by x<BR>\n" );
document.write( "(1+x)^5 - 1 = 5.704x<BR>\n" );
document.write( "A quadratic equation we can graph<BR>\n" );
document.write( "(1+x)^5 - 5.704x - 1 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-.1%2C+.1%2C+-.05%2C+.05%2C+%281%2Bx%29%5E5-5.704x-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-.1%2C+.1%2C+-.05%2C+.05%2C+%281%2Bx%29%5E5-5.704x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );