document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137563>Question 1137563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Monthly payments of $ 319.05 are made for 3 years to repay a loan at 7.6​% compounded monthly. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755447 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=755447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> payments made at the end of each month are 319.05.<BR>\n" );
document.write( "number of months = 3 years * 12 months per year = 36 months.<BR>\n" );
document.write( "percent interest rate per month= 7.6 / 12 = .633333333 percent.\r<BR>\n" );
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document.write( "use 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( "to find the present value of the loan (the loan amount), do the following:\r<BR>\n" );
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document.write( "set present value = 0<BR>\n" );
document.write( "set value = 0<BR>\n" );
document.write( "set number of time periods = 3 years * 12 = 36 months.<BR>\n" );
document.write( "set payment per month equal to -319.05<BR>\n" );
document.write( "set percent interest rate per month = 7.6% / 12 = .63333333%.<BR>\n" );
document.write( "set payments to be made at the end of each month.\r<BR>\n" );
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document.write( "click on pv and the calculator tells you that the present value of the loan is equal to $10,241.66.\r<BR>\n" );
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document.write( "that's the loan amount.\r<BR>\n" );
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document.write( "to find the future value of the loan, make the same inputs as for present value of the loan except click on fv rather than pv.\r<BR>\n" );
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document.write( "the calculator tells you that the future value of the loan is equal to $12,855.16.\r<BR>\n" );
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document.write( "the present+ value of the loan is how much you received from the bank.\r<BR>\n" );
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document.write( "the future value of the loan is how much the bank made from your payments.\r<BR>\n" );
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document.write( "the interest you paid on the loan is the sum of the payments minus the loan amount.<BR>\n" );
document.write( "that would be 319.05 * 36 - 10241.66 = 1244.14.\r<BR>\n" );
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document.write( "the interest the bank made on the loan payments you gave them is the future value of the loan minus the sum of the payments = 12855.16 - 319.05 * 36 = 1369.36.\r<BR>\n" );
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document.write( "the money they lent you is equivalent to them investing that money at 7.6% per year compounded monthly for 36 months.\r<BR>\n" );
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document.write( "the formula for that is f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "f is the future value.<BR>\n" );
document.write( "p is the present value - 10241.66<BR>\n" );
document.write( "r is the interest rate per time period = .076/12<BR>\n" );
document.write( "n is the number of time periods = 3 * 12 = 36\r<BR>\n" );
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document.write( "the formula becomes f = 10241.66 * (1 + .076/12) ^ 36 = 12855.16 rounded to the penny.\r<BR>\n" );
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document.write( "in the calculator, you make the payments negative because it's money going out.<BR>\n" );
document.write( "the present value and the future value are then positive because it's money coming in.<BR>\n" );
document.write( "the present value is money coming in to you.<BR>\n" );
document.write( "the future value is the money coming in to the bank.\r<BR>\n" );
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document.write( "if you had made the payments positive, the present value and the future value would have then shown as negative.\r<BR>\n" );
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document.write( "it's a calculator and cash flow convention.\r<BR>\n" );
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document.write( "here's what the calculator inputs and outputs look like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/032801.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/032802.jpg\" alt=\"$$$\">+\r<BR>\n" );
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document.write( " </SPAN>\n" );
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