document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118428>Question 1118428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Debts of $400.00, $450.00 and $500.00 are due in one year, eighteen months and thirty months from now respectively.\r<BR>\n" );
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document.write( "Determine the single payment now that would settle the debts if interest is 8% p.a. compounded quarterly.  Let the focal date be now. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733820 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=733820\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 400 is due in one year = 12 months.<BR>\n" );
document.write( "450 is due in 18 months.<BR>\n" );
document.write( "500 is due in 30 months.\r<BR>\n" );
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document.write( "the interest rate is 8% per year compounded quarterly.\r<BR>\n" );
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document.write( "8% per year compounded quarterly is equal to 8/4 = 2% per quarter.\r<BR>\n" );
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document.write( "there are 4 quarters in a year.\r<BR>\n" );
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document.write( "since a year is equal to 12 months, then there are 4 quarters in 12 months which means there are 3 months in a quarter.\r<BR>\n" );
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document.write( "you need to translate everything to quarters.\r<BR>\n" );
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document.write( "1 year * 4 = 4 quarters.\r<BR>\n" );
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document.write( "18 months / 3 = 6 quarters.\r<BR>\n" );
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document.write( "30 months / 3 = 10 quarters.\r<BR>\n" );
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document.write( "note that 18 months divided by 12 = 1.5 years * 4 = 6 quarters.\r<BR>\n" );
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document.write( "note also that 30 months divided by 12 = 2.5 years * 4 = 10 quarters.\r<BR>\n" );
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document.write( "it all checks out.\r<BR>\n" );
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document.write( "400 is due in 1 year = 4 quarters.\r<BR>\n" );
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document.write( "the interest rate is .02 per quarter.\r<BR>\n" );
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document.write( "divide 400 by 1.02^4 to get a present value of 369.5381704.\r<BR>\n" );
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document.write( "450 is due in 18 months = 1.5 years = 6 quarters.\r<BR>\n" );
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document.write( "divide 450 by 1.02^6 to get a present value of 399.587122.\r<BR>\n" );
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document.write( "500 is due in 30 months = 2.5 years = 10 quarters.\r<BR>\n" );
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document.write( "divide 500 by 1.02^10 to get a present value of 410.1741499.\r<BR>\n" );
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document.write( "take the sum of all 3 present values to get a combined present value of 1179.299442.\r<BR>\n" );
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document.write( "that amount invested at 2% per quarter will cover all 3 payments.\r<BR>\n" );
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document.write( "this can be seen in the following excel spreadsheet printout.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/061101.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "if they paid 1179.299442 today, that would be the equivalent of making the payments at the time indicated in the problem.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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