document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118761>Question 1118761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What amount is accumulated after 3 years of P6,500 invested at a rate of 12% per year compounded semi annually. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734190 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=734190\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 12% compounded semi-annually would be equal to 12/2 = 6% per semi-annual period.\r<BR>\n" );
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document.write( "the formula for compound interest is f = p * (1 + r) ^ n.\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period (months in this case).<BR>\n" );
document.write( "n is the number of time periods (months in this case).\r<BR>\n" );
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document.write( "in your problem, p = 6500, r = .12/2 = .06 per semi-annual period, n = 3 * 2 = 6 semi-annual periods.\r<BR>\n" );
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document.write( "the formula becomes 6500 = p * (1 + .06) ^ 6.\r<BR>\n" );
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document.write( "solve for p to get p = 6500 / ((1 + .06) ^ 6)\r<BR>\n" );
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document.write( "you get p = 4582.243513.\r<BR>\n" );
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document.write( "6500 = 4582.243513 * (1 + .06) ^ 6 becomes 6500 = 6500, confirming the solution is correct.\r<BR>\n" );
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document.write( "in these compounded interest rate calculations, if you are given the annual interest rate and the number of years, then:\r<BR>\n" );
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document.write( "interest rate per time period = annual interest rate divided by number of compounding periods per year.\r<BR>\n" );
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document.write( "number of time periods = number of years times number of compounding periods per year.\r<BR>\n" );
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document.write( "in your problem, you spefied compounding semi-annually.\r<BR>\n" );
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document.write( "that means 2 compounding periods per year.\r<BR>\n" );
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document.write( "12% / 2 = 6% per semi-annual period.<BR>\n" );
document.write( "3 years * 2 = 6 semi-annual periods.\r<BR>\n" );
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document.write( "in the formula, the interest rate percent is divided by 100 to get interest rate.\r<BR>\n" );
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document.write( "12% per year is there .12 per year.<BR>\n" );
document.write( "divide that by 2 and you get an interest rate of .06 per semi-annual period.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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