document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124449>Question 1124449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> George secured an adjustable-rate mortgage (ARM) loan to help finance the purchase of his home 5 years ago. The amount of the loan was $350,000 for a term of 30 years, with interest at the rate of 5%/year compounded monthly. Currently, the interest rate for his ARM is 3.5%/year compounded monthly, and George's monthly payments are due to be reset. What will be the new monthly payment? (Round your answer to the nearest cent.)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740768 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=740768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> adjustable rate mortgage mortgage was for $350,000 five years ago for a period of 30 years.\r<BR>\n" );
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document.write( "the rate was 3.5% per year compounded monthly.<BR>\n" );
document.write( "it will now be raised to 5% per year compounded monthly.\r<BR>\n" );
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document.write( "analysis is done using the following online financial calculator.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "the first step is to find out what the monthly payment would be for the $350,000 loan at 3.5% per year compounded monthly for 30 years.\r<BR>\n" );
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document.write( "the results of that analysis is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/092701.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "that analysis shows that the monthly payment are $1571.66.\r<BR>\n" );
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document.write( "the next step is to determine the remaining balance of the original loan after 5 years.\r<BR>\n" );
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document.write( "that is done by finding the present value of the mortgage at 3.5% per year compounded monthly for the remaining 25 years of the loan.\r<BR>\n" );
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document.write( "the results of that analysis are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/092702.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "that analysis shows that the remaining balance of the loan after 5 years is equal to $313,940.34.\r<BR>\n" );
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document.write( "that is the amount that will now be serviced at 5% per year compounded monthly for the remaining 25 years of the loan.\r<BR>\n" );
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document.write( "the next step is to determine what the monthly payments are to be for the remainder of the loan.\r<BR>\n" );
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document.write( "this is done by finding the monthly payments for a mortgage of $313,940.34 at 5% per year compounded monthly for the next 25 years.\r<BR>\n" );
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document.write( "the results of that analysis are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/092703.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "that analysis shows that the monthly payment will be $1835.26 for the next 25 years of the loan.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "i confirmed using the texas instruments BA-II business analyst calculator.\r<BR>\n" );
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document.write( "the difference between that calculator and the online calculator is that the BA-II doesn't round the answer, so it should technically be more accurate.\r<BR>\n" );
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document.write( "the BA-II showed some slight differences in the remaining balance of the loan after 5 years, but the subsequent analysis to find the monthly payment showed that the monthly payment agrees with the online calculator results when you round to 2 decimal places, so no discrepancy was noted.\r<BR>\n" );
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document.write( "we are talking very small differences.<BR>\n" );
document.write( "the online calculator said the remaining balance on the loan after 5 years was $313,940.35, while the texas instruments BA=II said the remaining balance on the loan after 5 years was $313,939.7545.\r<BR>\n" );
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document.write( "that's a difference of less than a thousandth of a percent.\r<BR>\n" );
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document.write( "seeing as both calculators gave the same monthly payment of $1835.26, i'd go with that.\r<BR>\n" );
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document.write( "when using the calculators, you use the percent interest rate, not the interest rate.\r<BR>\n" );
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document.write( "the percent interest rate is equal to 100 times the interest rate.<BR>\n" );
document.write( "the interest rate is the percent interest rate divided by 100.\r<BR>\n" );
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document.write( "in your problem, you were given the percent interest rate, so no modification of that part needed to be done.\r<BR>\n" );
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document.write( "you did have to convert the yearly percent interest rate to a monthly percent interest rate.\r<BR>\n" );
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document.write( "an annual percent interest rate of 3.5% per year is equal to a monthly percent interest rate of 3.5/12 = .291666666666666666.....% per month.\r<BR>\n" );
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document.write( "an annual percent interest rate of 5% per year is equal to a monthly percent interest rate of 5/12 = .4166666666666666666666....% per month.\r<BR>\n" );
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document.write( "you also needed to convert the number of years of the loan to number of months.\r<BR>\n" );
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document.write( "30 years * 12 = 360 months.\r<BR>\n" );
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document.write( "25 years * 12 = 300 months.\r<BR>\n" );
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document.write( "the inputs to online financial calculator for the different analyses are shown below:\r<BR>\n" );
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document.write( "first analysis was to find the monthly payment on the $350,000 loan for 30 years at 3.5% per year.\r<BR>\n" );
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document.write( "inputs were:<BR>\n" );
document.write( "present value = 350000<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of monthly periods = 360<BR>\n" );
document.write( "percent interest rate per month = .2916666666666666666<BR>\n" );
document.write( "payment is made at the end of each monthly period<BR>\n" );
document.write( "click on PMT to get -1,571.66<BR>\n" );
document.write( "it is shown as negative because it is money going out.<BR>\n" );
document.write( "the present value was shown as positive because it was money coming in.\r<BR>\n" );
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document.write( "second analysis was to find the remaining balance on the loan after 5 years.\r<BR>\n" );
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document.write( "all inputs were left unchanged from the first analysis except the number of monthly periods was changed from 360 to 300.<BR>\n" );
document.write( "click on PV to get 313,940.34\r<BR>\n" );
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document.write( "third analysis was to find the monthly payments for a loan of $313,940.34 for the remaining 25 years of the loan.\r<BR>\n" );
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document.write( "all inputs were left unchanged from the second analysis except the percent interest rate per month was changed from .291666666666666666 to .416666666666666666.<BR>\n" );
document.write( "click on PMT to get -1,835.26<BR>\n" );
document.write( "once again, payment is shown as negative because it's money going out.\r<BR>\n" );
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document.write( "i also used excel to show you the monthly transactions for the critical time periods of the loan.\r<BR>\n" );
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document.write( "that is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/092704.jpg\" alt = \"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/092705.jpg\" alt = \"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/092706.jpg\" alt = \"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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