document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886768>Question 886768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your annual income is $50,000. You want to take out a mortgage loan to buy a house. The rule on mortgage loan requires that your annual mortgage payment cannot exceed 30% of your annual income. If the current interest rate is 5% for a 30-year mortgage loan, what is the maximum amount one can borrow for a house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536131 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=536131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> income is $50,000<BR>\n" );
document.write( "annual mortgage payment cannot exceed 30% of your annual income.<BR>\n" );
document.write( "current interest rate is 5% per year for a 30 year mortgage loan.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "30% of $50,000 = $15,000 which is the most payments you can make per year on the mortgage.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since mortgage payments are made monthly, divide that $15,000 by 12 and you get a maximum payment of $1250.00 per month.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "interest rate of 5% per year becomes interest rate of 5% / 12 = .41666666667% per momnth.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "number of months becomes 30 * 12 = 360 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your payment cannot exceed $1250.00 per month.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "present value of a monthly payment of $1250.00 for 360 months at .4166666667% per month would be equal to $232,852.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that is the maximum mortgage the bank will allow you.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to solve this problem you need to find the formula for the present value of a payment which is also called the present value of an annuity.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you also need to put everything in months since mortgages are typically paid per month.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you divide the interest rate by 12 and you multiply the number of years by 12.<BR>\n" );
document.write( "the interest rate is the interest rate percent divided by 100.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.investopedia.com/articles/03/101503.asp\" target = \"_blank\">http://www.investopedia.com/articles/03/101503.asp</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in this reference you are looking for the formula for PV of an ordinary annuity.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i assumed months.<BR>\n" );
document.write( "if you are working in years, then the problem becomes different.<BR>\n" );
document.write( "your maximum payment is still $15,000 per year.<BR>\n" );
document.write( "your payments are $15,000 a year for 30 years.<BR>\n" );
document.write( "this would come out to be a present value of a payment of $15,000 for 30 years at 5% interest which would be equal to $230,587.<BR>\n" );
document.write( "that would be your maximum mortgage if you paid once a year and the interest was compounded once per year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you use the same PV of an ordinary annuity formula but pmt is now $15,000 and interest rate is now .05 and number of time periods is now 30.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );