document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162050>Question 1162050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Chapter: Amount of Annuity\r<BR>\n" );
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document.write( "You wish to purchase 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785747 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=785747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Future value annuity formula:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%28%281%2B%28r%2Fn%29%29%5E%28nt%29-1%29%2F%28r%2Fn%29 ALIGN=MIDDLE  ALT=\"A+=+P%28%281%2B%28r%2Fn%29%29%5E%28nt%29-1%29%2F%28r%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A = future value<BR>\n" );
document.write( "P = periodic contribution<BR>\n" );
document.write( "r = annual interest rate<BR>\n" );
document.write( "n = number of compounding periods per year<BR>\n" );
document.write( "t = time (years)<br><BR>\n" );
document.write( "Note those parameter definitions mean<br><BR>\n" );
document.write( "r/n = periodic interest rate<BR>\n" );
document.write( "1+r/n = periodic growth factor<BR>\n" );
document.write( "nt = number of compounding periods<br><BR>\n" );
document.write( "In this example,<br><BR>\n" );
document.write( "A = 200,000<BR>\n" );
document.write( "P = the unknown<BR>\n" );
document.write( "r = 5% = .05<BR>\n" );
document.write( "n = 2<BR>\n" );
document.write( "t = 12<BR>\n" );
document.write( "r/n = .025<BR>\n" );
document.write( "1+r/n = 1.025<BR>\n" );
document.write( "nt = 24<br><BR>\n" );
document.write( "I'll let you get the practice in doing the calculations....<br><BR>\n" );
document.write( "It's very easy to get ridiculous answers if you get decimal points or parentheses in the wrong place; make sure your answer makes sense.<br><BR>\n" );
document.write( "You should get an answer of a little under $6200.  That makes sense because not counting the interest $6200 every 6 months for 12 years is $6200*24 = $148,800; it's reasonable that the accrued interest will bring that up to the desired $200,000.<br><BR>\n" );
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