document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193410>Question 1193410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Julita owes Jose the following amounts:<BR>\n" );
document.write( "a. 55,000 at the end of 4 years,<BR>\n" );
document.write( "b. 48,000 at the end of 5 years, and<BR>\n" );
document.write( "c. 75,000 due in 3 years from today at 9% converted quarterly.<BR>\n" );
document.write( "What single payment at the end of 2 years will settle Julita’s <BR>\n" );
document.write( "obligations if money is worth 15% converted monthly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848807 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate the Present Value of Each Obligation at the End of 2 Years**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Obligation a: 55,000 at the end of 4 years**<BR>\n" );
document.write( "    * Time to maturity from the end of 2 years: 4 - 2 = 2 years<BR>\n" );
document.write( "    * Present Value (PV_a) = 55,000 / (1 + 0.15/12)^(2*12) \r<BR>\n" );
document.write( "\n" );
document.write( "* **Obligation b: 48,000 at the end of 5 years**<BR>\n" );
document.write( "    * Time to maturity from the end of 2 years: 5 - 2 = 3 years<BR>\n" );
document.write( "    * Present Value (PV_b) = 48,000 / (1 + 0.15/12)^(3*12)\r<BR>\n" );
document.write( "\n" );
document.write( "* **Obligation c: 75,000 due in 3 years from today at 9% converted quarterly**<BR>\n" );
document.write( "    * Time to maturity from today: 3 years<BR>\n" );
document.write( "    * Time to maturity from the end of 2 years: 3 - 2 = 1 year<BR>\n" );
document.write( "    * Effective annual rate for quarterly compounding: (1 + 0.09/4)^4 - 1 = 0.093083<BR>\n" );
document.write( "    * Present Value (PV_c) = 75,000 / (1 + 0.093083)^1 * (1 + 0.15/12)^(-12) \r<BR>\n" );
document.write( "\n" );
document.write( "**2. Calculate the Total Present Value of All Obligations at the End of 2 Years**\r<BR>\n" );
document.write( "\n" );
document.write( "* Total Present Value = PV_a + PV_b + PV_c\r<BR>\n" );
document.write( "\n" );
document.write( "**3. Determine the Single Payment at the End of 2 Years**\r<BR>\n" );
document.write( "\n" );
document.write( "* The single payment at the end of 2 years to settle all obligations is equal to the total present value of all obligations at that time.\r<BR>\n" );
document.write( "\n" );
document.write( "**Using Python:**\r<BR>\n" );
document.write( "\n" );
document.write( "```python<BR>\n" );
document.write( "import numpy as np\r<BR>\n" );
document.write( "\n" );
document.write( "# Calculate the present value of each obligation at the end of 2 years\r<BR>\n" );
document.write( "\n" );
document.write( "# Obligation a: 55,000 at the end of 4 years<BR>\n" );
document.write( "# Time to maturity from the end of 2 years: 4 - 2 = 2 years<BR>\n" );
document.write( "pv_a = 55000 / (1 + 0.15/12)**(2*12) \r<BR>\n" );
document.write( "\n" );
document.write( "# Obligation b: 48,000 at the end of 5 years<BR>\n" );
document.write( "# Time to maturity from the end of 2 years: 5 - 2 = 3 years<BR>\n" );
document.write( "pv_b = 48000 / (1 + 0.15/12)**(3*12)\r<BR>\n" );
document.write( "\n" );
document.write( "# Obligation c: 75,000 due in 3 years from today at 9% converted quarterly<BR>\n" );
document.write( "# Time to maturity from today: 3 years<BR>\n" );
document.write( "# Time to maturity from the end of 2 years: 3 - 2 = 1 year<BR>\n" );
document.write( "# Effective annual rate for quarterly compounding: (1 + 0.09/4)**4 - 1 = 0.093083<BR>\n" );
document.write( "pv_c = 75000 / (1 + 0.093083)**1 * (1 + 0.15/12)**(-12) \r<BR>\n" );
document.write( "\n" );
document.write( "# Total present value of all obligations at the end of 2 years<BR>\n" );
document.write( "total_pv = pv_a + pv_b + pv_c\r<BR>\n" );
document.write( "\n" );
document.write( "print(f\"Single payment at the end of 2 years to settle Julita's obligations: {total_pv:.2f}\") <BR>\n" );
document.write( "```\r<BR>\n" );
document.write( "\n" );
document.write( "**Result:**\r<BR>\n" );
document.write( "\n" );
document.write( "The single payment at the end of 2 years to settle Julita's obligations is approximately **130,623.40**.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );