document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134809>Question 1134809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Angela wants to buy a house for 700000.she has a deposit of 50000 and take 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<BR>\n" );
document.write( "borrow from the bank?<BR>\n" );
document.write( "2.calculate the monthly payment if she wishes to settle the loan in 15 years <BR>\n" );
document.write( "3.Angela later won the lottery and wishes to settle the loan after the 50th payment.what is the outstanding balance? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752304 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=752304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the house costs 700,000 and she has a deposit of 50,000.\r<BR>\n" );
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document.write( "the interest rate on the loan is 18% compounded monthly.\r<BR>\n" );
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document.write( "she puts her 50,000 down and she needs to borrow the remainder from the bank.\r<BR>\n" );
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document.write( "that remainder is equal to 700,000 - 50,000 = 650,000.\r<BR>\n" );
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document.write( "you can use a financial calculator to determine the monthly paymentw.\r<BR>\n" );
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document.write( "the one i use is the TI-BA-II.\r<BR>\n" );
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document.write( "using this calculator, i provide the following inputs.\r<BR>\n" );
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document.write( "present value is equal to 650,000.<BR>\n" );
document.write( "percent interest rate per month is equal to 18/12 = 1.5.<BR>\n" );
document.write( "number of months is equal to 15 * 12 = 180.<BR>\n" );
document.write( "future value is equal to 0.<BR>\n" );
document.write( "payments are made at the end of each month.\r<BR>\n" );
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document.write( "i then have the calculator tell me that the monthly payments are 10,467.736767 dollars payable at the end of each month, which would be rounded to 10,467.74 dollars.\r<BR>\n" );
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document.write( "if i want to know the remaining balance at the end of the 50th month, the financial calculator has the capability to tell me that directly, or i can figure it out by doing the following.\r<BR>\n" );
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document.write( "since there are 180 months in the loan, then after the 50th month, i have 180 - 50 = 130 months of payments left.\r<BR>\n" );
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document.write( "i use the calculator again and input the following.\r<BR>\n" );
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document.write( "present value = 0<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of months = 130<BR>\n" );
document.write( "percent interest rate per month = 1.5<BR>\n" );
document.write( "payment at the end of each month is equal to 10,467.73676.\r<BR>\n" );
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document.write( "i then have the calculator tell me that the present value of that loan is equal to 597,115.126 dollars.\r<BR>\n" );
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document.write( "that's the remaining balance after 50 months which is what i would have to pay to settle the loan.\r<BR>\n" );
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document.write( "there is a manual formula i can use to calculate the same thing.\r<BR>\n" );
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document.write( "that formula is shown below.\r<BR>\n" );
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document.write( "the first formula i would use is:\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( "the inputs to this formula would be:\r<BR>\n" );
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document.write( "p = 650,000 (without the comma)<BR>\n" );
document.write( "r = .18 / 12 = .015 (this is the rate, not the percent)<BR>\n" );
document.write( "n = 12 * 15 = 180\r<BR>\n" );
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document.write( "the formula would become:\r<BR>\n" );
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document.write( "a = (650000*.015)/(1-(1/(1+.015)^180)).\r<BR>\n" );
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document.write( "the result from executing this formula in my calculator would be 10,467.74676.\r<BR>\n" );
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document.write( "this compares favorably with what the calculator told me.                                                                                       \r<BR>\n" );
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document.write( "the second formula i would use is:\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( "the inputs to this formula would be:\r<BR>\n" );
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document.write( "a = 10,467.73676<BR>\n" );
document.write( "r = .015<BR>\n" );
document.write( "n= 180 - 50 = 130\r<BR>\n" );
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document.write( "the formula would then look like this:\r<BR>\n" );
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document.write( "p = (10,467.73676*(1-1/(1+.015)^130))/.015\r<BR>\n" );
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document.write( "i would enter it into my calculator exactly as shown.\r<BR>\n" );
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document.write( "it would then tell me that the present value is equal to 597,115.1262.\r<BR>\n" );
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document.write( "this compares favorably with what the financial calculator told me.\r<BR>\n" );
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document.write( "i can also do the calculations in excel and show you the month by month breakdown of the payments and the remaining in each time payment.\r<BR>\n" );
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document.write( "this provides a reasonable confirmation that the calculations were done correctly.\r<BR>\n" );
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document.write( "this is what the excel printout looks like.\r<BR>\n" );
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document.write( "i skipped non-essential months since they weren't necessary for you to understand what i was trying to show you.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021502.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021503.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the formula used in excel to calculate the monthly payments was:\r<BR>\n" );
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document.write( "=PMT(0.18/12,15*12,-F3)\r<BR>\n" );
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document.write( ".18/12 was the rate per month.<BR>\n" );
document.write( "15*12 was the number of months.<BR>\n" );
document.write( "-F3 was the negative value of the contents that were in cell F3.\r<BR>\n" );
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document.write( "finally, there is a function in the TI-BA-II that allows you to find the remaining balance at the end of the 50th month directly.\r<BR>\n" );
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document.write( "using this method, i was able to confirm that my other calculations were correct.\r<BR>\n" );
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document.write( "if you don't have a financial calculator handy, there is an online calculator you can use.\r<BR>\n" );
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document.write( "that calculator can be found at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "you should be able to duplicate my findings using this calculator, give or take a few pennies because of rounding.\r<BR>\n" );
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document.write( "if you are having trouble duplicating these answers, let me know and i'll guide you through it in more detail.\r<BR>\n" );
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document.write( "the tutorial where i got the manual formulas from can be found here:\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#f9\" target = \"_blank\">https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f9</a> </SPAN>\n" );
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