document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203536>Question 1203536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate selling price of a house if:<BR>\n" );
document.write( "They paid 21082.00 down<BR>\n" );
document.write( "payments are 682.00 per month for 30 years<BR>\n" );
document.write( "interest rate 6.6% is compounded monthly </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852258 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52810)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Calculate selling price of a house if:<BR>\n" );
document.write( "They paid 21082.00 down<BR>\n" );
document.write( "payments are 682.00 per month for 30 years<BR>\n" );
document.write( "interest rate 6.6% is compounded monthly <BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This my solution goes second after the solution by @Theo.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;@Theo used an online calculator in his solution.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Since this web-site is to teach Math, the expected solution should be mathematical.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, I present here a standard mathematical solution.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculator can be used as a secondary tool for verification.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Then the sequence of steps would be normally educative.\r<BR>\n" );
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document.write( "In this problem, we are given the monthly payment for the loan;\r\n" );
document.write( "the annual interest rate and the duration of the loan.\r\n" );
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document.write( "Having this input information, we can find the loaned amount.\r\n" );
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document.write( "Use the formula for the monthly payment for a loan\r\n" );
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document.write( "    M = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2A%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29 ALIGN=MIDDLE  ALT=\"L%2A%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "where L is the loan amount; r  is the effective interest rate per month;\r\n" );
document.write( "n is the number of payments (same as the number of months); M is the monthly payment.\r\n" );
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document.write( "From this formula, express for the loan amount \r\n" );
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document.write( "    L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%2F%28%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29%29 ALIGN=MIDDLE  ALT=\"M%2F%28%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "In this problem  M = $682;  r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.066%2F12 ALIGN=MIDDLE  ALT=\"0.066%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  n = 30*12 = 360 monthly payments.\r\n" );
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document.write( "Substitute these values into the formula and get for the maximum loan amount\r\n" );
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document.write( "    L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=682%2F%28%28%280.066%2F12%29%2F%281-%281%2B0.066%2F12%29%5E%28-360%29%29%29%29 ALIGN=MIDDLE  ALT=\"682%2F%28%28%280.066%2F12%29%2F%281-%281%2B0.066%2F12%29%5E%28-360%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = $106,786.28.\r\n" );
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document.write( "To find the celling price of the house, we should add the down payment to this value\r\n" );
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document.write( "    the celling price = $106,786.28 + $21,082.00 = $127,868.281\r\n" );
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document.write( "<U>ANSWER</U>.  The selling price of the house is $127,868  (rounded to the closest dollar).\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "Notice that my numbers precisely coincide with the numbers in the post by @Theo, so you can consider it as a check.\r<BR>\n" );
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document.write( "In such calculations, it is important to avoid intermediate rounding.<BR>\n" );
document.write( "Rounding can be done at the end, only.\r<BR>\n" );
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document.write( "Intermediate rounding is PROHIBITED, since it leads to wrong answer.\r<BR>\n" );
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document.write( "Also, a calculator should provide the necessary precision.\r<BR>\n" );
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document.write( "I use MS Excel in my computer. It works with 15 decimals in mantissa <BR>\n" );
document.write( "and provides the necessary precision.\r<BR>\n" );
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document.write( "I simply copy-paste my numerical formula into Excel spreadsheet and get the answer in one click.\r<BR>\n" );
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document.write( "Many standard online calculators provide the necessary precision.\r<BR>\n" );
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document.write( "You may use, for example, this free-of-charge online calculator\r<BR>\n" );
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document.write( "https://www.calculatorsoup.com/calculators/financial/loan-calculator.php\r<BR>\n" );
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document.write( "It is reliable, has convenient user-friendly interface, has complete instructions and descriptions, <BR>\n" );
document.write( "provides the necessary precision and was checked million times. You may use it to check my/your calculations.\r<BR>\n" );
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document.write( "There is another (= one more) reason why I produced and placed my solution here.\r<BR>\n" );
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document.write( "@Theo' posts used visual plots to support his solutions.<BR>\n" );
document.write( "These plots were integral inseparable part of his solutions.<BR>\n" );
document.write( "But some time ago, Theo left this forum and stopped supporting web-site with his plots.<BR>\n" );
document.write( "As a result, you see now some colored spots in his posts, where his plots should be.<BR>\n" );
document.write( "Due to this reason, @Theo's posts lost their educational meaning and value.<BR>\n" );
document.write( "Therefore, I create my posts with my own mathematical solutions<BR>\n" );
document.write( "to replace @Theo' solutions and provide meaningful mathematical content.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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