document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193454>Question 1193454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the rate compounded semi-annually if 30,000 is the present value<BR>\n" );
document.write( "of 55,000 due at the end of 4 years. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825492 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=825492\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> present value is 30,000<BR>\n" );
document.write( "future value is 55,000<BR>\n" );
document.write( "time period is 4 years * 2 semi-annual periods per year = 8 semi-annual time periods.\r<BR>\n" );
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document.write( "formula is f = p * g ^ n<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "g is the growth factor per time period<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "formula becomes:<BR>\n" );
document.write( "55,000 = 30,000 * g ^ 8<BR>\n" );
document.write( "divide both sides of the equation by 30,000 to get:<BR>\n" );
document.write( "55,000 / 30,000 = g ^ 8<BR>\n" );
document.write( "simplify a little to get:<BR>\n" );
document.write( "55/30 = g ^ 8<BR>\n" );
document.write( "take the 8th root of both sides of the equation to get:<BR>\n" );
document.write( "(55/30)^(1/8) = g<BR>\n" );
document.write( "solve for g to get:<BR>\n" );
document.write( "g =  1.078711179 per semi-annual period.<BR>\n" );
document.write( "since g = 1 + r, solve for r to get:<BR>\n" );
document.write( "r = g - 1 = .078711179 per semi-annual period.<BR>\n" );
document.write( "multiply by 2 to get .1574223574 per year.<BR>\n" );
document.write( "multiply by 100 to get 15.74223574% per year.<BR>\n" );
document.write( "that is the annual rate compounded semi-annually that will get 30,000 to grow to 55,000 at the end of 4 years.<BR>\n" );
document.write( "to solve the problem, you divide that rate by 2 to get the rate per semi-annual period and you multiply the number of years by 2 to get the number of semi-annual periods.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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