document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109824>Question 1109824</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A couple wishes to borrow money using the equity in their home for collateral. A loan company will loan them up to&#8203; 70% of their equity. They puchased their home 9 years ago for &#8203;$70,391. The home was financed by paying 15&#8203;% down and signing a 15&#8203;-year mortgage at 9.3&#8203;% on the unpaid balance. Equal monthly payments were made to amortize the loan over the 15&#8203;-year period. The net market value of the house is now&#8203; $100,000. After making their 108th &#8203;payment, they applied to the loan company for the maximum loan. How much&#8203; (to the nearest&#8203; dollar) will they&#8203; receive? \r<BR>\n" );
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document.write( "Thank you in advance.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724758 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=724758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "L = amount of money loaned out (principal)<BR>\n" );
document.write( "L = 85% of initial home value (since 15% is already paid down)<BR>\n" );
document.write( "L = 85% of $70,391<BR>\n" );
document.write( "L = 0.85*70391<BR>\n" );
document.write( "L = 59832.35<BR>\n" );
document.write( "So the mortgage balance starts at $59,832.35 (this is the amount of money loaned to the couple)\r<BR>\n" );
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document.write( "The annual interest rate is r = 9.3% = 0.093<BR>\n" );
document.write( "The monthly interest rate is c = r/12 = 0.093/12 = 0.00775\r<BR>\n" );
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document.write( "The mortgage is set for y = 15 years, which is n = 12*y = 12*15 = 180 months\r<BR>\n" );
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document.write( "I'm going to use the second formula mentioned on <a  rel=nofollow HREF=\"https://www.mtgprofessor.com/formulas.htm\">this page</a>\r<BR>\n" );
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document.write( "The formula mentioned is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+%28L%2A%28%281%2Bc%29%5En-%281%2Bc%29%5EP%29%29%2F%28%281%2Bc%29%5En-1%29 ALIGN=MIDDLE  ALT=\"B+=+%28L%2A%28%281%2Bc%29%5En-%281%2Bc%29%5EP%29%29%2F%28%281%2Bc%29%5En-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which will help us find the balance B after the number of months p\r<BR>\n" );
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document.write( "So we'll plug in...<BR>\n" );
document.write( "L = 59832.35<BR>\n" );
document.write( "c = 0.00775<BR>\n" );
document.write( "n = 180<BR>\n" );
document.write( "p = 108<BR>\n" );
document.write( "and that leads us to the balance being...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+%28L%2A%28%281%2Bc%29%5En-%281%2Bc%29%5Ep%29%29%2F%28%281%2Bc%29%5En-1%29 ALIGN=MIDDLE  ALT=\"B+=+%28L%2A%28%281%2Bc%29%5En-%281%2Bc%29%5Ep%29%29%2F%28%281%2Bc%29%5En-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+%2859832.35%2A%28%281%2B0.00775%29%5E180-%281%2B0.00775%29%5E108%29%29%2F%28%281%2B0.00775%29%5E180-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+33980.2387672002 ALIGN=MIDDLE  ALT=\"B+=+33980.2387672002\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+33980.24 ALIGN=MIDDLE  ALT=\"B+=+33980.24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the balance after the 108th payment is $33,980.24\r<BR>\n" );
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document.write( "A = Appraised Value<BR>\n" );
document.write( "A = 100,000<BR>\n" );
document.write( "B = Balance on mortgage (aka: amount of money still needed to be paid back)<BR>\n" );
document.write( "B = 33,980.24 (calculated above)<BR>\n" );
document.write( "E = Home Equity Value<BR>\n" );
document.write( "E = A - B<BR>\n" );
document.write( "E = 100,000 - 33,980.24<BR>\n" );
document.write( "E = 66,019.76\r<BR>\n" );
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document.write( "We now know the home equity value. So we simply take 70% of this to find the max loan amount<BR>\n" );
document.write( "70% of E = 0.7*E = 0.7*66019.76 = 46,213.832 = 46,213.83<BR>\n" );
document.write( "which rounds to 46,214 when rounding to the nearest dollar\r<BR>\n" );
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document.write( "Final Answer: <font color=red>$46,214</font>\r<BR>\n" );
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