document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196116>Question 1196116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Paul owes Winston R1000 due in three years and R8000 due in five years. He wishes to reschedule so as to pay two sums on different dates, one say x in one year, and the other 2x five years later. Winston agrees provided that the interest rate is 18% per annum compound quarterly. What are Paul's payments? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848423 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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=848423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find the Present Value of Paul's Current Debt**\r<BR>\n" );
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document.write( "* **Calculate the Present Value of R1000 due in 3 years:**<BR>\n" );
document.write( "    * **Quarterly Interest Rate:** 18% per annum / 4 quarters = 4.5% per quarter <BR>\n" );
document.write( "    * **Number of Quarters:** 3 years * 4 quarters/year = 12 quarters<BR>\n" );
document.write( "    * **Present Value:** R1000 / (1 + 0.045)^12 = R1000 / 1.71 = R584.79\r<BR>\n" );
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document.write( "* **Calculate the Present Value of R8000 due in 5 years:**<BR>\n" );
document.write( "    * **Number of Quarters:** 5 years * 4 quarters/year = 20 quarters<BR>\n" );
document.write( "    * **Present Value:** R8000 / (1 + 0.045)^20 = R8000 / 2.4117 = R3317.79\r<BR>\n" );
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document.write( "* **Total Present Value of Debt:** R584.79 + R3317.79 = R3902.58\r<BR>\n" );
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document.write( "**2. Set Up the Equation for the Rescheduled Debt**\r<BR>\n" );
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document.write( "* **Present Value of x due in 1 year:** x / (1 + 0.045)^4 <BR>\n" );
document.write( "* **Present Value of 2x due in 5 years:** 2x / (1 + 0.045)^20 \r<BR>\n" );
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document.write( "* **Equation:**<BR>\n" );
document.write( "    * x / (1 + 0.045)^4 + 2x / (1 + 0.045)^20 = R3902.58\r<BR>\n" );
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document.write( "**3. Solve for x**\r<BR>\n" );
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document.write( "* **Simplify the equation:**<BR>\n" );
document.write( "    * x / 1.1925 + 2x / 2.4117 = R3902.58<BR>\n" );
document.write( "    * 0.8386x + 0.8295x = R3902.58<BR>\n" );
document.write( "    * 1.6681x = R3902.58\r<BR>\n" );
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document.write( "* **Calculate x:**<BR>\n" );
document.write( "    * x = R3902.58 / 1.6681 <BR>\n" );
document.write( "    * x ≈ R2338.69\r<BR>\n" );
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document.write( "**4. Calculate the Second Payment**\r<BR>\n" );
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document.write( "* 2x = 2 * R2338.69 = R4677.38\r<BR>\n" );
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document.write( "**Therefore, Paul's rescheduled payments will be:**\r<BR>\n" );
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document.write( "* **R2338.69 due in one year**<BR>\n" );
document.write( "* **R4677.38 due in five years**\r<BR>\n" );
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document.write( "**Note:** These calculations assume that the interest rate remains constant at 18% per annum compounded quarterly throughout the entire period.<BR>\n" );
document.write( " </SPAN>\n" );
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