document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193456>Question 1193456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose 80,000 is due at the end of 4 years with interest at 10%<BR>\n" );
document.write( "compounded quarterly. If money is worth 14% compounded quarterly,<BR>\n" );
document.write( "what is the value of obligation,<BR>\n" );
document.write( "a. Now,<BR>\n" );
document.write( "b. At the end of 3 years, and<BR>\n" );
document.write( "c. At the end of 6.5 years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848663 by </B><A HREF=/tutors/aboutme.mpl?userid=yurtman><B>yurtman(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=yurtman><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate the Future Value of the Obligation:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Given:**<BR>\n" );
document.write( "    * Principal: $80,000<BR>\n" );
document.write( "    * Interest Rate: 10% per year compounded quarterly (0.10/4 = 0.025 per quarter)<BR>\n" );
document.write( "    * Number of Periods: 4 years * 4 quarters/year = 16 quarters\r<BR>\n" );
document.write( "\n" );
document.write( "* **Formula:**<BR>\n" );
document.write( "    * Future Value (FV) = Principal * (1 + Interest Rate per Period)^(Number of Periods)<BR>\n" );
document.write( "    * FV = $80,000 * (1 + 0.025)^16<BR>\n" );
document.write( "    * FV = $80,000 * 1.50945 <BR>\n" );
document.write( "    * FV = $120,756\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Calculate the Present Value of the Obligation:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **a. Now:**<BR>\n" );
document.write( "    * **Discount Rate:** 14% per year compounded quarterly (0.14/4 = 0.035 per quarter)<BR>\n" );
document.write( "    * **Number of Periods:** 4 years * 4 quarters/year = 16 quarters\r<BR>\n" );
document.write( "\n" );
document.write( "    * **Formula:**<BR>\n" );
document.write( "        * Present Value (PV) = Future Value / (1 + Discount Rate per Period)^(Number of Periods)<BR>\n" );
document.write( "        * PV = $120,756 / (1 + 0.035)^16<BR>\n" );
document.write( "        * PV = $120,756 / 1.7947<BR>\n" );
document.write( "        * PV = $67,278.31\r<BR>\n" );
document.write( "\n" );
document.write( "* **b. At the end of 3 years:**<BR>\n" );
document.write( "    * **Future Value at the end of 3 years:** $120,756 (calculated above)<BR>\n" );
document.write( "    * **Discount Period:** 1 year * 4 quarters/year = 4 quarters\r<BR>\n" );
document.write( "\n" );
document.write( "    * **Formula:**<BR>\n" );
document.write( "        * PV = Future Value / (1 + Discount Rate per Period)^(Number of Periods)<BR>\n" );
document.write( "        * PV = $120,756 / (1 + 0.035)^4<BR>\n" );
document.write( "        * PV = $120,756 / 1.1475<BR>\n" );
document.write( "        * PV = $105,220.41\r<BR>\n" );
document.write( "\n" );
document.write( "* **c. At the end of 6.5 years:**<BR>\n" );
document.write( "    * **Future Value at the end of 6.5 years:** $120,756 (calculated above)<BR>\n" );
document.write( "    * **Discount Period:** (6.5 - 4) years * 4 quarters/year = 10 quarters\r<BR>\n" );
document.write( "\n" );
document.write( "    * **Formula:**<BR>\n" );
document.write( "        * PV = Future Value / (1 + Discount Rate per Period)^(Number of Periods)<BR>\n" );
document.write( "        * PV = $120,756 / (1 + 0.035)^10<BR>\n" );
document.write( "        * PV = $120,756 / 1.4106<BR>\n" );
document.write( "        * PV = $85,613.59\r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **a. Value of obligation now:** $67,278.31<BR>\n" );
document.write( "* **b. Value of obligation at the end of 3 years:** $105,220.41<BR>\n" );
document.write( "* **c. Value of obligation at the end of 6.5 years:** $85,613.59<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );