document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185410>Question 1185410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You wish to purchased a house for $200,000 in 12 years. You can invest your money at 5%/a compounded semiannually. How much do you need to invest every 6 months, starting in 6 months, so that you will have $200,000 at the time of your last deposit? (Hint: You need to find the value for \"a\". ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816225 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=816225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can use a financial calculator to solve this.\r<BR>\n" );
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document.write( "your inputs are shown below.\r<BR>\n" );
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document.write( "your output is shown below.\r<BR>\n" );
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document.write( "you can also solve this by formula.\r<BR>\n" );
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document.write( "the formula is:\r<BR>\n" );
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document.write( "a = (f*r)/((1+r)^n-1)\r<BR>\n" );
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document.write( "a is the annuity.<BR>\n" );
document.write( "f is the future amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "for your problem.\r<BR>\n" );
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document.write( "f = 200,000 (without the comma.<BR>\n" );
document.write( "r is the interest rate per time period = .05/2 = .025 per semi-annual time period.<BR>\n" );
document.write( "n is the number of time periods = 12 * 2 = 24 semi-annual time periods.\r<BR>\n" );
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document.write( "a = (f*r)/((1+r)^n-1) becomes:\r<BR>\n" );
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document.write( "a = (200000*.025)/((1+.025)^24-1) = 6182.564072.\r<BR>\n" );
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document.write( "this is the same as what the calculator tells you when rounded to 2 decimal places.\r<BR>\n" );
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document.write( "the calculator says the payment at the end of each semi-annual period is equal to 6182.56.\r<BR>\n" );
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document.write( "https://arachnoid.com/finance/index.html<BR>\n" );
document.write( "the calculator can be found at <a  rel=nofollow HREF= \"\" target = \"_blank\">https://arachnoid.com/finance/index.html</a>\r<BR>\n" );
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