document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140679>Question 1140679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Angela wants to buy a house for R700000.She has a deposit of R50000 and takes out a loan for the balance at a rate of 18% p.a compounded monthly.\r<BR>\n" );
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document.write( "(1) How much money must Angela borrow from the bank? \r<BR>\n" );
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document.write( "(2) Calculate the monthly payment if she wishes to settle to settle the loan in 15 years. \r<BR>\n" );
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document.write( "(3) Angela later won the lottery and wished to settle the loan after the 50th payment.What is the outstanding balance?\r<BR>\n" );
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document.write( "Please help me I begg   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761203 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=761203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the price of the house if 700,000<BR>\n" );
document.write( "the deposit is 50,000<BR>\n" );
document.write( "the mortgage is therefore 700,000 minus 50,000 = 650,000.\r<BR>\n" );
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document.write( "i used the texas instruments business analyst 2 (TI-BA-II).\r<BR>\n" );
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document.write( "inputs were:\r<BR>\n" );
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document.write( "present value = 650,000<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "interest rate = 18% per year / 12 =  1.5% per month.<BR>\n" );
document.write( "number of months = 15 years * 12 = 180 months.<BR>\n" );
document.write( "payments are made at the end of each month.\r<BR>\n" );
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document.write( "calculator says that the end of month payments need to be 10,467.73676.\r<BR>\n" );
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document.write( "after the 50th payment, there are 180 - 50 = 130 months left to pay.\r<BR>\n" );
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document.write( "to find out what the remaining balance is after the 50th payment, you need to find the present value of the payments for 130 months.\r<BR>\n" );
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document.write( "inputs to the calculator would be:\r<BR>\n" );
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document.write( "present value = 0<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "payment at the end of each month = 10,467.73676.<BR>\n" );
document.write( "interest rate = 18% per year / 12 = 1.5% per month.<BR>\n" );
document.write( "payments are made at the end of each month.\r<BR>\n" );
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document.write( "calculator says that the present value is equal to 597,115.126.\r<BR>\n" );
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document.write( "that's the outstanding remaining balance after 50 payments.\r<BR>\n" );
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document.write( "i did the analysis in excel and it confirms the results.\r<BR>\n" );
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document.write( "here's the display of the excel month by month analysis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/050801.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/050802.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/050803.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "you can do the same analysis with the following online calculator if you don't have one available.\r<BR>\n" );
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document.write( "<  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "there are also formulas you can use at the following reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#formulas\" target = \"_blank\">https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#formulas</a>\r<BR>\n" );
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document.write( "formula you would use are:\r<BR>\n" );
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document.write( "ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "a = (p*r)/(1-(1/(1+r)^n)) \r<BR>\n" );
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document.write( "a is the annuity.<BR>\n" );
document.write( "p is the present amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods. \r<BR>\n" );
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document.write( "and then:\r<BR>\n" );
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document.write( "PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "p = (a*(1-1/(1+r)^n))/r \r<BR>\n" );
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document.write( "p is the present value of the annuity.<BR>\n" );
document.write( "a is the annuity.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods. \r<BR>\n" );
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document.write( "when you use the online calculator:\r<BR>\n" );
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document.write( "if you enter the present value as positive, the payment will show up as negative.\r<BR>\n" );
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document.write( "interest rate are in percent form, just as i did using the TI-BA-II.\r<BR>\n" );
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document.write( "results are rounded to the nearest penny, unlike what the TI-BA-II gives me.\r<BR>\n" );
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document.write( "when you use the formulas.\r<BR>\n" );
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document.write( "interest rate is not in percent form.\r<BR>\n" );
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document.write( "that means that 18%  would be shown as .18 and 1.5% would be shown as .015.\r<BR>\n" );
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document.write( "all numbers are positive.\r<BR>\n" );
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document.write( "all parentheses need to be entered in your calculator exactly as shown.\r<BR>\n" );
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document.write( "if you have any problems or questions on any of this, write to dtheophilis@gmail.com.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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