document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193367>Question 1193367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kindly requesting your help about homework.<BR>\n" );
document.write( "1. Marry owes 500 due in eight months, for each of the following cases, what single payment will his debt if simple interest rate is 15%p.a.<BR>\n" );
document.write( "1.1.1. Now<BR>\n" );
document.write( "1.1.2. Six months from now.<BR>\n" );
document.write( "1.1.3. in one year.\r<BR>\n" );
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document.write( "2. A promissory note dated 1 April 2021 for 15000, borrowed at a simple discount rate of 16%p.a. due on the 1 October 2021 is sold on the 1 July 2021<BR>\n" );
document.write( "2.1.1. what is the maturity value of the note?<BR>\n" );
document.write( "2.1.2. What is the present value on the date of sale? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848667 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=848667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's break down the calculations for these debt scenarios.\r<BR>\n" );
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document.write( "**1. Marry's Debt**\r<BR>\n" );
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document.write( "**1.1.1. Present Value of the Debt Now**\r<BR>\n" );
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document.write( "* **Given:** <BR>\n" );
document.write( "    * Future Value (FV) = 500 <BR>\n" );
document.write( "    * Interest Rate (r) = 15% per year = 0.15 <BR>\n" );
document.write( "    * Time (t) = 8 months = 8/12 years = 2/3 years\r<BR>\n" );
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document.write( "* **Simple Interest:** <BR>\n" );
document.write( "    * Interest = Principal * Rate * Time <BR>\n" );
document.write( "    * Interest = 500 * 0.15 * (2/3) = 50 \r<BR>\n" );
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document.write( "* **Present Value (PV):** <BR>\n" );
document.write( "    * PV = FV - Interest <BR>\n" );
document.write( "    * PV = 500 - 50 <BR>\n" );
document.write( "    * PV = 450\r<BR>\n" );
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document.write( "**Therefore, the single payment Marry needs to make now is 450.**\r<BR>\n" );
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document.write( "**1.1.2. Present Value of the Debt Six Months from Now**\r<BR>\n" );
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document.write( "* **Time Remaining:** 8 months - 6 months = 2 months = 2/12 years = 1/6 years\r<BR>\n" );
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document.write( "* **Future Value (FV) at 6 months from now:** 500 (remains the same)\r<BR>\n" );
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document.write( "* **Simple Interest:** <BR>\n" );
document.write( "    * Interest = 500 * 0.15 * (1/6) = 12.50\r<BR>\n" );
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document.write( "* **Present Value (PV) at 6 months from now:** <BR>\n" );
document.write( "    * PV = FV - Interest <BR>\n" );
document.write( "    * PV = 500 - 12.50 <BR>\n" );
document.write( "    * PV = 487.50\r<BR>\n" );
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document.write( "**Therefore, the single payment Marry needs to make six months from now is 487.50.**\r<BR>\n" );
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document.write( "**1.1.3. Present Value of the Debt in One Year**\r<BR>\n" );
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document.write( "* **Time Remaining:** 8 months - 12 months = -4 months (This means the due date has already passed)\r<BR>\n" );
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document.write( "* **Since the due date has already passed, Marry would need to pay the full amount plus interest accrued for the past 4 months.**\r<BR>\n" );
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document.write( "* **Interest Accrued:** 500 * 0.15 * (4/12) = 25\r<BR>\n" );
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document.write( "* **Total Payment:** 500 + 25 = 525\r<BR>\n" );
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document.write( "**Therefore, if the payment is due in one year, Marry needs to pay 525.**\r<BR>\n" );
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document.write( "**2. Promissory Note**\r<BR>\n" );
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document.write( "**2.1.1. Maturity Value of the Note**\r<BR>\n" );
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document.write( "* **Given:** <BR>\n" );
document.write( "    * Principal (P) = 15000 <BR>\n" );
document.write( "    * Discount Rate (r) = 16% per year = 0.16 <BR>\n" );
document.write( "    * Time (t) = 6 months (April 1 to October 1) = 6/12 years = 0.5 years\r<BR>\n" );
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document.write( "* **Discount:** <BR>\n" );
document.write( "    * Discount = P * r * t <BR>\n" );
document.write( "    * Discount = 15000 * 0.16 * 0.5 <BR>\n" );
document.write( "    * Discount = 1200\r<BR>\n" );
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document.write( "* **Maturity Value (MV):** <BR>\n" );
document.write( "    * MV = Principal - Discount <BR>\n" );
document.write( "    * MV = 15000 - 1200 <BR>\n" );
document.write( "    * MV = 13800\r<BR>\n" );
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document.write( "**Therefore, the maturity value of the note is 13800.**\r<BR>\n" );
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document.write( "**2.1.2. Present Value on the Date of Sale (July 1, 2021)**\r<BR>\n" );
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document.write( "* **Time Remaining to Maturity:** 3 months (July 1 to October 1) = 3/12 years = 0.25 years\r<BR>\n" );
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document.write( "* **Discount from Sale Date:** <BR>\n" );
document.write( "    * Discount = Maturity Value * r * t <BR>\n" );
document.write( "    * Discount = 13800 * 0.16 * 0.25 <BR>\n" );
document.write( "    * Discount = 552\r<BR>\n" );
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document.write( "* **Present Value on the Date of Sale:** <BR>\n" );
document.write( "    * Present Value = Maturity Value - Discount <BR>\n" );
document.write( "    * Present Value = 13800 - 552 <BR>\n" );
document.write( "    * Present Value = 13248\r<BR>\n" );
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document.write( "**Therefore, the present value of the note on the date of sale (July 1, 2021) is 13248.**<BR>\n" );
document.write( " </SPAN>\n" );
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