document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006877>Question 1006877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The formula A=P(1+r)^2 gives the amount A in dollars that P dollars will grow to in 2 years at interest rate r (where r is given as a decimal), using compound interest. What interest rate will cause $1000 to grow to $1092.03 in 2 years? Round your answer to the nearest tenth of a percent if needed.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622922 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=622922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is A = P * (1+r)^2\r<BR>\n" );
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document.write( "P = 1000<BR>\n" );
document.write( "r = the annual interest rate<BR>\n" );
document.write( "A = 1092.03\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "1092.03 = 1000 * (1+r)^2\r<BR>\n" );
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document.write( "divide both sides of this equation by 1000 to get:\r<BR>\n" );
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document.write( "1092.03 / 1000 = (1+r)^2\r<BR>\n" );
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document.write( "raise both sides of that equation to the power of 1/2 to get:\r<BR>\n" );
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document.write( "(1092.03 / 1000) ^ (1/2) = 1 + r\r<BR>\n" );
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document.write( "the expression on the right side of the equation becomes 1 + r because:\r<BR>\n" );
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document.write( "((1+r)^2)^(1/2) becomes (1+r)^(2 * 1/2) which becomes (1+r)^1 which becomes 1+r.\r<BR>\n" );
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document.write( "subtract 1 from both sides of this equation to get:\r<BR>\n" );
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document.write( "(1092.03 / 1000) ^ (1/2) - 1 = r\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = .045002392\r<BR>\n" );
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document.write( "confirm by replacing r in the original equation with .045002392 to get:\r<BR>\n" );
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document.write( "1092.03 = 1000 * (1.045002392)^2 which becomes:\r<BR>\n" );
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document.write( "1092.03 = 1092.03, confirming the solution is correct.\r<BR>\n" );
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document.write( "1.\r<BR>\n" );
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document.write( "your solution is r = .045002392\r<BR>\n" );
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document.write( "the percent is 100 * .045002392 = 4.5002392%.\r<BR>\n" );
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document.write( "round that to the nearest tenth of a percent and your solution becomes:\r<BR>\n" );
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document.write( "r = 4.5%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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