document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955652>Question 955652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose $20,000 is invested into an account where interest is compounded semiannually. After 30 years the balance is $231,165.\r<BR>\n" );
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document.write( "What was the interest rate as a percent?\r<BR>\n" );
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document.write( "Round the answer to the nearest hundredth of a percent.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854601 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53937)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Suppose $20,000 is invested into an account where interest is compounded semiannually. <BR>\n" );
document.write( "After 30 years the balance is $231,165.<BR>\n" );
document.write( "What was the interest rate as a percent?<BR>\n" );
document.write( "Round the answer to the nearest hundredth of a percent.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The answer \"2.082%\" in the post by @lwsshar3 is incorrect and is FAR from to be true.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to bring a correct solution.\r<BR>\n" );
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document.write( "Compound Interest Formula: A=P(1+r/n)^nt, <BR>\n" );
document.write( "P=initial investment, <BR>\n" );
document.write( "r=interest rate, <BR>\n" );
document.write( "n=number of compounding periods per year, <BR>\n" );
document.write( "A=amt after t-years\r<BR>\n" );
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document.write( "For given problem:<BR>\n" );
document.write( "P=20000<BR>\n" );
document.write( "r=interest rate(to be determined)<BR>\n" );
document.write( "n=2<BR>\n" );
document.write( "t=30<BR>\n" );
document.write( "A=amt after 30 yrs<BR>\n" );
document.write( "...<BR>\n" );
document.write( "231165 = 20000(1+r/2)^2*30<BR>\n" );
document.write( "231165/20000 = (1+r/2)^60<BR>\n" );
document.write( "11.5583 = (1+r/2)^60<BR>\n" );
document.write( "raise both sides to the 1/60th power<BR>\n" );
document.write( "1.04163 = 1+r/2<BR>\n" );
document.write( "r/2 = 1.04163-1 = 0.0416333<BR>\n" );
document.write( "r = 0.0416333*2 = 0.0832667 = 8.32667%, approximately.<BR>\n" );
document.write( "What was the interest rate as a percent? 8.32667%\r<BR>\n" );
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document.write( "<U>CHECK</U>.  &nbsp;&nbsp;Future value is  &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20000%2A%281%2B0.0832667%2F2%29%5E60 ALIGN=MIDDLE  ALT=\"20000%2A%281%2B0.0832667%2F2%29%5E60\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 231165.26.\r<BR>\n" );
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document.write( "Solved correctly.\r<BR>\n" );
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