document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050473>Question 1050473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have a home mortgage of $180,000 with a fixed APR of 4% for 30 years.<BR>\n" );
document.write( "A) For month #1 what would the payment, interest, principal and the balance be?<BR>\n" );
document.write( "For month #2 what would the payment, interest, principal, and the balance be?<BR>\n" );
document.write( "For month#3 what would the payment, interest, principal, and the balance be?<BR>\n" );
document.write( "For month #4 what would the payment, interest, principal, and the balance be?<BR>\n" );
document.write( "B) What do you notice about the payment toward the principal during the term of the loan?<BR>\n" );
document.write( "C) What do you notice about the payment toward interest during the term of the loan? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #666345 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=666345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can use a time value of money to figure out what the monthly payment would be.<BR>\n" );
document.write( "one such calculator can be found here:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://arachnoid.com/finance/index.html\" target = \"_blank\">http://arachnoid.com/finance/index.html</a>\r<BR>\n" );
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document.write( "you would enter present value as -180,000<BR>\n" );
document.write( "you would enter future value as 0.<BR>\n" );
document.write( "you would enter interest rate at 4/12 percent = .333333<BR>\n" );
document.write( "you would enter number of time periods as 30 * 12 = 360<BR>\n" );
document.write( "you would enter payment as 0 or just leave it alone.<BR>\n" );
document.write( "you would select end of period payments.<BR>\n" );
document.write( "you would then select pmt and the calculator will tell you what the monthly payment is.\r<BR>\n" );
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document.write( "i truncated to 6 decimal digits which is usually enough accuracy to get a rough idea.\r<BR>\n" );
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document.write( "my inputs to this calculator look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/100101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "my output from the calculator look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/100102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the calculator tells me that the monthly payment is 859.35.\r<BR>\n" );
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document.write( "i verified with another financial calculator that this is correct.\r<BR>\n" );
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document.write( "the month by month calculations are done as follows:\r<BR>\n" );
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document.write( "start with 180,000 as the mortgage amount.<BR>\n" );
document.write( "that's the remaining balance at the beginning of the first month.\r<BR>\n" );
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document.write( "at the end of the first month the following happens:\r<BR>\n" );
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document.write( "interest = 4/1200 * 180,000 = 600.<BR>\n" );
document.write( "payment = 859.35<BR>\n" );
document.write( "principal reduction = 859.35 - 600 = 259.35<BR>\n" );
document.write( "remaining balance = 179740.65.\r<BR>\n" );
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document.write( "at the end of the second month the following happens:<BR>\n" );
document.write( "interest = 4/1200 * 179740.65 = 599.1355<BR>\n" );
document.write( "payment = 859.35<BR>\n" );
document.write( "principal reduction = 859.35 - 599.1355 = 260.2145<BR>\n" );
document.write( "remaining balance = 179480.4355.\r<BR>\n" );
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document.write( "you do this for 4 months and you get:\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "month    remaining balance         interest       payment        principal\r\n" );
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document.write( "0            $180,000.00             $0.00          $0.00          $0.00\r\n" );
document.write( "1            $179,740.65             $600.00        $859.35        $259.35\r\n" );
document.write( "2            $179,480.44             $599.14        $859.35        $260.21\r\n" );
document.write( "3            $179,219.36             $598.27        $859.35        $261.08\r\n" );
document.write( "4            $178,957.41             $597.40        $859.35        $261.95\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "what you notice is that, as each month goes by, the interest part of the payment is less and the principal part of the payment is more.\r<BR>\n" );
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document.write( "this is because, as the remaining balance gets smaller, the interest on that remaining balance is smaller.\r<BR>\n" );
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document.write( "since the payment is a fixed amount each month, the principal part of the loan gets bigger.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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