document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173104>Question 1173104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Michael Sanchez purchased a condominium for $73,000. He made a 20% down payment and financed the balance with a 30 year, 5% fixed-rate mortgage. (Round your answers to the nearest cent.\r<BR>\n" );
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document.write( "What is the amount (in $) of the monthly principal and interest portion, PI, of Michael's loan?\r<BR>\n" );
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document.write( "I was able to get the monthly payment of 392.01 and a down payment of 14,600. Not sure what the next step is.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798316 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=798316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> price of the condo was 73,000.<BR>\n" );
document.write( "20% down was 73,000 * .2 = 14,600.<BR>\n" );
document.write( "amount to be financed was 73,000 - 14,600 = 58,400.<BR>\n" );
document.write( "30 year loan at 5% per year nominal results in:<BR>\n" );
document.write( "360 month loan at (5/12)% per month.<BR>\n" );
document.write( "financial calculator says that the payment at the end of each month needs to be 313.50.<BR>\n" );
document.write( "not sure where you got 392.01 from, but that's not correct.<BR>\n" );
document.write( "a payment of 392.01 for 360 months at 5% per year compounded monthly is for a loan of 73,024.<BR>\n" );
document.write( "looks like you financed the whole thing rather than the net balance after paying the down payment.<BR>\n" );
document.write( "my calculations indicate the payment at the end of each month needs to be 313.50.<BR>\n" );
document.write( "it's actually 313.5038278 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "the amount in dollars of the monthly payment that is principal and interest varies throughout the loan.<BR>\n" );
document.write( "at the start of the loan the interest is a much higher percentage of the payment.<BR>\n" );
document.write( "at the end of the loan, the principal is a much higher percentage of the payment.\r<BR>\n" );
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document.write( "you cannot come up with a fixed percentage of each monthly payment.<BR>\n" );
document.write( "you can, however, come up with an average based on the total payments.<BR>\n" );
document.write( "the monthly payment are 313.50 rounded to the nearest penny.<BR>\n" );
document.write( "the total payments are 360 * 313.50 = 112,860<BR>\n" );
document.write( "total principal paid is 58,400<BR>\n" );
document.write( "total payments made is 112,860.<BR>\n" );
document.write( "total interest paid is 112,860 minus 58,400 = 54,460.<BR>\n" );
document.write( "average amount of equity in each payment would be equal to 58,400/112,860 = 51.75% rounded to 2 decimal places.<BR>\n" );
document.write( "average amount of interest in each payment would be equal to 54,460/112,860 = 48.25% rounded to 2 decimal places.\r<BR>\n" );
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document.write( "as stated before, the actual amount of equity in each payment increases as the loan matures.\r<BR>\n" );
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document.write( "the following excerpts from an excel analysis show this to be true.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/011602.jpg\" >\r<BR>\n" );
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document.write( "from this excel printout, the interest portion of the payment starts off as 77.6% of the current payment and 77.6% of the cumulative sum of the current payments.<BR>\n" );
document.write( "the interest portion of the payments ends up as .41% of the current payment and 48.26% of the cumulative sum of the current payments.\r<BR>\n" );
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document.write( "my calculations showed 48.25% and the excel showed 48.26%.<BR>\n" );
document.write( "the difference is in rounding.<BR>\n" );
document.write( "i used the payment that was rounded to 2 decimal places.<BR>\n" );
document.write( "excel used the more detailed payment which was probably rounded to a whole lot more decimal places.\r<BR>\n" );
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document.write( "the point of the excel presentation is that the percent of the payment that is equity and interest changes as the loan progresses through its life cycle.<BR>\n" );
document.write( "if you want a fixed percentage, then it has to be an average from the sum of all payments\r<BR>\n" );
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document.write( "i'll be available to answer any questions you might have about this.<BR>\n" );
document.write( "theo<BR>\n" );
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