document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189735>Question 1189735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person purchased a ​$198741 home 10 years ago by paying ​20% down and signing a​ 30-year mortgage at 11.4​% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20​-year mortgage at  compounded 6.6% monthly. How much interest will refinancing​ save?\r<BR>\n" );
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document.write( "Money Saved: $\r<BR>\n" );
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document.write( "Please Help! Thank you :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821488 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'm using the formulas found on this page<BR>\n" );
document.write( "https://www.mtgprofessor.com/formulas.htm\r<BR>\n" );
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document.write( "The home value is $198,741.<BR>\n" );
document.write( "20% of it is paid off through the downpayment, so 80% is remaining<BR>\n" );
document.write( "0.80*198741 = 158,992.80\r<BR>\n" );
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document.write( "This is the loan amount L<BR>\n" );
document.write( "L = 158,992.80\r<BR>\n" );
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document.write( "For the original mortgage at 11.4%, the monthly rate c is<BR>\n" );
document.write( "c = r/12 = 0.114/12 = 0.0095<BR>\n" );
document.write( "and the number of months is n = 360 because 30*12 = 360.\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "L = 158,992.80<BR>\n" );
document.write( "c = 0.0095<BR>\n" );
document.write( "n = 360<BR>\n" );
document.write( "Plug those values into the first formula mentioned in that link above. You should get a monthly payment of P = 1562.37\r<BR>\n" );
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document.write( "Plug those values into the second formula along with lowercase p = 120 (since 10 years = 120 months) to find that B = 147,456.55<BR>\n" );
document.write( "Unfortunately that link uses uppercase P to represent payment and lowercase p to denote the number of months paid into; the letter choice may seem a bit confusing. \r<BR>\n" );
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document.write( "Anyways, we get B = 147,456.55 which is the unpaid balance at year 10. This is the starting point, and we'll have two branching options\r<BR>\n" );
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document.write( "starting balance = 147,456.55\r<BR>\n" );
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document.write( "Mortgage A (interest rate = 11.4%)<BR>\n" );
document.write( "monthly payment = 1562.37<BR>\n" );
document.write( "total amount paid back = (240 months)*(1562.37 per month) = 374,968.80<BR>\n" );
document.write( "m = Total interest paid <BR>\n" );
document.write( "m = 374,968.80 - 147,456.55<BR>\n" );
document.write( "m = 227,512.25\r<BR>\n" );
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document.write( "Mortgage B (interest rate = 6.6%)<BR>\n" );
document.write( "monthly payment = 1108.09 <BR>\n" );
document.write( "total amount paid back = (240 months)*(1108.09 per month) = 265,941.60<BR>\n" );
document.write( "n = Total interest paid <BR>\n" );
document.write( "n = 265,941.60 - 147,456.55<BR>\n" );
document.write( "n = 118,485.05\r<BR>\n" );
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document.write( "m-n = amount of interest saved by going with mortgage B<BR>\n" );
document.write( "m-n = 227,512.25 - 118,485.05<BR>\n" );
document.write( "m-n = <font color=red>109,027.20</font>\r<BR>\n" );
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document.write( "Answer: <font color=red>$109,027.20</font><BR>\n" );
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