document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286379>Question 286379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company wants to set up a sinking fund for the repayment of a loan of 100million at the end of four years.It makes equal deposits at the end of each month into a fund that earns interest at 22% per year compounded monthly.  Determine the size of each deposit and construct a sinking fund schedule(the first three months only) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207697 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=207697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Loan is $100 million to be repaid at the end of 4 years.<BR>\n" );
document.write( "Monthly deposits are made.<BR>\n" );
document.write( "Interest rate is 22% per year compounded monthly.\r<BR>\n" );
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document.write( "This is a Payment for a Future Value type problem.\r<BR>\n" );
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document.write( "Using a financial calculator, you would enter:\r<BR>\n" );
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document.write( "Number of Time periods = 4 * 12 = 48<BR>\n" );
document.write( "Interest Rate per Time Period = 22% / 100% = .22 / 12 = .0183333333 <BR>\n" );
document.write( "Future Amount = $100 million<BR>\n" );
document.write( "Payments are made at the end of each month.<BR>\n" );
document.write( "You are looking for the payment amount.\r<BR>\n" );
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document.write( "Your answer would be (using the financial calculator)\"\r<BR>\n" );
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document.write( "Payment is $1,317,274.45 per month.\r<BR>\n" );
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document.write( "Sinking Fund Balance for the first 3 months would be:\r<BR>\n" );
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document.write( "(1+i) = 1.0183333333 per month<BR>\n" );
document.write( "p = $1,317,274.45 per month\r<BR>\n" );
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document.write( "End of month 1 = $1,317,274.456<BR>\n" );
document.write( "End of month 2 = $1,317,274.456 * (1+i) = $1,341,424.482 + p = $2,658,698.932<BR>\n" );
document.write( "End of month 3 = $2,658,698.932 * (1+i) = $2,707,441.746 + p = $4,024,716.196<BR>\n" );
document.write( ".....<BR>\n" );
document.write( "End of month 47 = $96,906,113.47 * (1+i) = $98,682,725.55 + p = $100,000,000.00\r<BR>\n" );
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document.write( "If you do not have a financial calculator, you can get an online version that will help you do the same problem.\r<BR>\n" );
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document.write( "As a last resort, you can use the formula given in the following lesson on Payment for a Future Value.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.algebra.com/algebra/homework/Finance/PMTFV.lesson\" target = \"_blank\">PAYMENT FOR A FUTURE VALUE</a>\r<BR>\n" );
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document.write( "The equation to use from that lesson is:\r<BR>\n" );
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document.write( "PAYMENT FOR A FUTURE VALUE EQUATION\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PMT%28FV%29+=+%28FV+%2F+%28%28%28%28%281%2Bi%29%5En-1%29%29%2Fi%29%29%29+ ALIGN=MIDDLE  ALT=\"+PMT%28FV%29+=+%28FV+%2F+%28%28%28%28%281%2Bi%29%5En-1%29%29%2Fi%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "PMT = Payment per Time Period<BR>\n" );
document.write( "FV = Future Value<BR>\n" );
document.write( "i = Interest Rate per Time Period<BR>\n" );
document.write( "n = Number of Time Periods\r<BR>\n" );
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document.write( "FV = $100,000,000<BR>\n" );
document.write( "i = .22 / 12 = .01833333333<BR>\n" );
document.write( "n = 12*4 = 48\r<BR>\n" );
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document.write( "Intermediate calculations would be:\r<BR>\n" );
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document.write( "(1.01833333333)^48 - 1 = 1.391762614\r<BR>\n" );
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document.write( "Equation would become:\r<BR>\n" );
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document.write( "PMT = 100,000,000 / (1.391762614/.01833333333) which would become:\r<BR>\n" );
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document.write( "PMT = $1,317,274.45\r<BR>\n" );
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document.write( "An online financial calculator that will also calculate this for you can be found at the following link:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.arachnoid.com/lutusp/finance.html\" target = \"_blank\">http://www.arachnoid.com/lutusp/finance.html</a>\r<BR>\n" );
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document.write( "You enter the information that you have and you click on the value you are looking for.\r<BR>\n" );
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document.write( "For example:\r<BR>\n" );
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document.write( "I entered values for:\r<BR>\n" );
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document.write( "Future Value.<BR>\n" );
document.write( "Interest Rate per time period.<BR>\n" );
document.write( "Number of time periods.<BR>\n" );
document.write( "Present Value (I set it equal to 0).\r<BR>\n" );
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document.write( "I set the payment to be made  at the end of the time period.\r<BR>\n" );
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document.write( "I then clicked on the button for Payment.\r<BR>\n" );
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document.write( "I got the same result that I gave you using both my own financial calculator plus solving the equation from the lesson.\r<BR>\n" );
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document.write( "One last item.\r<BR>\n" );
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document.write( "All equations used here assume re-investment of the interest earned each month.\r<BR>\n" );
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document.write( "That re-investment is assumed to be at the same interest rate used for calculating the payment.\r<BR>\n" );
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document.write( "I used Excel to calculate the money accruing in the sinking fund for every time period, not just the first 3.\r<BR>\n" );
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document.write( "The results are shown below:\r<BR>\n" );
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document.write( "Time Period	\r\n" );
document.write( "      Present Value of Loan	\r\n" );
document.write( "                         Payment	\r\n" );
document.write( "                                         Interest Rate	\r\n" );
document.write( "                                                        Sinking Fund Balance\r\n" );
document.write( "0     $41,810,169.363		         0.018333333	$0.000\r\n" );
document.write( "1	                 1,317,274.450		        $1,317,274.450\r\n" );
document.write( "2                        1,317,274.450		        $2,658,698.932\r\n" );
document.write( "3		         1,317,274.450		        $4,024,716.196\r\n" );
document.write( "4		         1,317,274.450		        $5,415,777.110\r\n" );
document.write( "5		         1,317,274.450		        $6,832,340.807\r\n" );
document.write( "6		         1,317,274.450		        $8,274,874.839\r\n" );
document.write( "7		         1,317,274.450		        $9,743,855.328\r\n" );
document.write( "8		         1,317,274.450		        $11,239,767.126\r\n" );
document.write( "9		         1,317,274.450		        $12,763,103.974\r\n" );
document.write( "10		         1,317,274.450		        $14,314,368.663\r\n" );
document.write( "11		         1,317,274.450		        $15,894,073.206\r\n" );
document.write( "12		         1,317,274.450		        $17,502,738.998\r\n" );
document.write( "13		         1,317,274.450		        $19,140,896.997\r\n" );
document.write( "14		         1,317,274.450		        $20,809,087.892\r\n" );
document.write( "15		         1,317,274.450		        $22,507,862.287\r\n" );
document.write( "16		         1,317,274.450		        $24,237,780.879\r\n" );
document.write( "17		         1,317,274.450		        $25,999,414.646\r\n" );
document.write( "18		         1,317,274.450		        $27,793,345.031\r\n" );
document.write( "19		         1,317,274.450		        $29,620,164.140\r\n" );
document.write( "20		         1,317,274.450		        $31,480,474.933\r\n" );
document.write( "21		         1,317,274.450		        $33,374,891.424\r\n" );
document.write( "22		         1,317,274.450		        $35,304,038.884\r\n" );
document.write( "23		         1,317,274.450		        $37,268,554.047\r\n" );
document.write( "24		         1,317,274.450		        $39,269,085.321\r\n" );
document.write( "25		         1,317,274.450		        $41,306,293.002\r\n" );
document.write( "26		         1,317,274.450		        $43,380,849.491\r\n" );
document.write( "27		         1,317,274.450		        $45,493,439.515\r\n" );
document.write( "28		         1,317,274.450		        $47,644,760.357\r\n" );
document.write( "29		         1,317,274.450		        $49,835,522.080\r\n" );
document.write( "30		         1,317,274.450		        $52,066,447.769\r\n" );
document.write( "31		         1,317,274.450		        $54,338,273.761\r\n" );
document.write( "32		         1,317,274.450		        $56,651,749.897\r\n" );
document.write( "33		         1,317,274.450		        $59,007,639.762\r\n" );
document.write( "34		         1,317,274.450		        $61,406,720.942\r\n" );
document.write( "35		         1,317,274.450		        $63,849,785.276\r\n" );
document.write( "36		         1,317,274.450	 	        $66,337,639.123\r\n" );
document.write( "37		         1,317,274.450		        $68,871,103.624\r\n" );
document.write( "38		         1,317,274.450		        $71,451,014.974\r\n" );
document.write( "39		         1,317,274.450		        $74,078,224.699\r\n" );
document.write( "40		         1,317,274.450		        $76,753,599.935\r\n" );
document.write( "41		         1,317,274.450		        $79,478,023.717\r\n" );
document.write( "42		         1,317,274.450		        $82,252,395.269\r\n" );
document.write( "43		         1,317,274.450		        $85,077,630.299\r\n" );
document.write( "44		         1,317,274.450		        $87,954,661.305\r\n" );
document.write( "45		         1,317,274.450		        $90,884,437.879\r\n" );
document.write( "46		         1,317,274.450		        $93,867,927.024\r\n" );
document.write( "47		         1,317,274.450		        $96,906,113.470\r\n" );
document.write( "48		         1,317,274.450		        $100,000,000.000\r\n" );
document.write( "</PRE> </SPAN>\n" );
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