document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096881>Question 1096881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To save for retirement karla harby put $650 each month into an ordinary annuity for 14 years. Interest was compounded monthly. At the end of the 14 years, the annuity was worth $154,986. What annual interest rate did she receive?\r<BR>\n" );
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document.write( "Please answer with Full Details.\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711301 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=711301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>The formula for the value P of an annuity with regular deposits of amount A, n times per year for t years, at an annual interest rate of r, is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+A%28%281%2Br%2Fn%29%5E%28nt%29-1%29%2F%28r%2Fn%29 ALIGN=MIDDLE  ALT=\"P+=+A%28%281%2Br%2Fn%29%5E%28nt%29-1%29%2F%28r%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In your problem, we know A is 650, n is 12, and t is 14; we need to find r.  The formula is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=154986+=+650%28%281%2Br%2F12%29%5E%2812%2A14%29-1%29%2F%28r%2F12%29 ALIGN=MIDDLE  ALT=\"154986+=+650%28%281%2Br%2F12%29%5E%2812%2A14%29-1%29%2F%28r%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If you know the interest rate r and 3 of the other 4 numbers, you can calculate the missing number using the formula, or some form of it.  But the interest rate r occurs in two different places in the formula, making it impossible to do a direct calculation to find the interest rate, if it is the unknown in the problem.<br><BR>\n" );
document.write( "So all you can do is use some mathematical tool, like a graphing calculator, to find the answer.  I used my TI-84 calculator to graph the two functions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=154986 ALIGN=MIDDLE  ALT=\"154986\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=650%28%281%2Bx%29%5E%2812%2A14%29-1%29%2F%28x%29 ALIGN=MIDDLE  ALT=\"650%28%281%2Bx%29%5E%2812%2A14%29-1%29%2F%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and used the intersection of the two graphs to find the monthly interest rate is 0.00398 = 0.398%, making the annual interest rate 0.04776 = 4.776%. </SPAN>\n" );
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