document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169507>Question 1169507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a firm will need 300000 at the end of 3 years to repay a loan. the firm decided that it would deposit 20000 at the start of each quarter during these 3 years into the account. the account yield 12% per annum compounded quarterly during the first year. what rate of interest should it earn during the remaining 2 years to accumulate enough amount into this account to pay the loan at the end of 3 years.(Answer:13.8%) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794262 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=794262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i did a cash flow analysis using excel, the results of which are shown below.\r<BR>\n" );
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document.write( "the time periods are in quarters from time period 0 to time period 12. (3 years * 4 time periods per year = 12 time periods)\r<BR>\n" );
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document.write( "twelve investments of 20,000 each are made from time period 0 to time period 11.\r<BR>\n" );
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document.write( "for time periods 0 to 4, the investments are made at 3% interest rate per time period (12% per year / 4 = 3% per quarter = 3% per time period).\r<BR>\n" );
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document.write( "the total invested in time period 4 is 106,182.72.\r<BR>\n" );
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document.write( "it is shown as minus because it's money that is going out.\r<BR>\n" );
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document.write( "in effect, you have 106,182.72 in your account in time period 4.<BR>\n" );
document.write( "that amount is positive, but you immediately turn around and invest that for the next 8 quarters, so it becomes money going out.\r<BR>\n" );
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document.write( "that's why it is shown as negative.\r<BR>\n" );
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document.write( "the cash flow for the next 8 time periods is 106,182.72 going out in time period 4 plus 20,000 going out in time period 5 through time period 11.\r<BR>\n" );
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document.write( "in time period 12, you need to have 300,000 coming in, so that amount is entered as positive in time period 12.\r<BR>\n" );
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document.write( "the internal rate of return analysis is done for time periods 4 through 12 inclusive.\r<BR>\n" );
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document.write( "it comes out to be 3.45% rounded to two decimal places.\r<BR>\n" );
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document.write( "the equivalent annual rate of return is 3.45 * 4 = 13.8% per year.\r<BR>\n" );
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document.write( "here's a reference on how the internal rate of return is calculated manually.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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