document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119012>Question 1119012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A debt of x, with interest rate of 7% compounded annually will be retired at the end of 10 years through the accumulation of deposit in the sinking fund invested at 6% compounded semi-annually. The deposit in the sinking fund every end of six months is 21,962.68. What is the value of x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734553 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=734553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the future value of your investment of 21,962.68 at the end of every 6 month period for 10 years is equal to $590,145.44, according to the results of the financial calculator i used at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "that is the just enough to pay off your debt at that time.\r<BR>\n" );
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document.write( "the future value of your debt at 7% per year compounded anually is equal to x * 1.07^10 = 1.967151357 * x.\r<BR>\n" );
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document.write( "therefore 1.967151357 * x = 590,145.44.\r<BR>\n" );
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document.write( "solve for x to get x = 590,145.44 / 1.967151357 = 300,000.0167.\r<BR>\n" );
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document.write( "this can be rounded to 300,000 dollars, which should be your answer.\r<BR>\n" );
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document.write( "the future value of your debt of 300,000.0167 today is equal to 300,000.0167 * 1.07 ^ 10 = 590145.44.\r<BR>\n" );
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document.write( "the future value of your semi-annual payments into the sinking fund is exactly equal to that as shown in the following printout.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/062501.jpg\" alt = \"$$$\" >\r<BR>\n" );
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document.write( "the inputs to that calculator were:\r<BR>\n" );
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document.write( "present value = 0<BR>\n" );
document.write( "number of time periods = 10 years * 2 payments per year = 20 semi-annual time periods.<BR>\n" );
document.write( "the payment made at the end of each semi-annual period is 21962.68.<BR>\n" );
document.write( "the interest rate per time period is 6% per year / 2 semi-annual periods per year = 3% per semi-annual time period.<BR>\n" );
document.write( "the payments are made at the end of each semi-annual time period.\r<BR>\n" );
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document.write( "the output of that calculator is:\r<BR>\n" );
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document.write( "future value = 590,145.44.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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