document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193311>Question 1193311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with the homework.<BR>\n" );
document.write( "1. Mr farmer needs to make the following payments against a loan on his truck:<BR>\n" );
document.write( "10000 after six months,20000 after one year,40000 after two years. Due to drought,he could not make the first two payments.after 18 months, Mr farmer immediately make a down payment of 50000 against the loan.<BR>\n" );
document.write( "1.1. Draw a timeline to represent the above mentioned scenario<BR>\n" );
document.write( "1.2. What single payment should he make two years from now to settle his debt if a simple interest rate of 17% is applied on all the amounts.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848713 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52838)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Please help me with the homework.<BR>\n" );
document.write( "1. Mr farmer needs to make the following payments against a loan on his truck:<BR>\n" );
document.write( "10000 after six months, 20000 after one year, 40000 after two years. <BR>\n" );
document.write( "Due to drought, he could not make the first two payments. <BR>\n" );
document.write( "After 18 months, Mr farmer immediately make a down payment of 50000 against the loan.<BR>\n" );
document.write( "1.1. Draw a timeline to represent the above mentioned scenario<BR>\n" );
document.write( "1.2. What single payment should he make two years from now to settle his debt <BR>\n" );
document.write( "     if a simple interest rate of 17% is applied on all the amounts.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I believe that\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"10000 after six months, 20000 after one year, 40000 after two years\" \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;in the post means\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"10000 six months from now, 20000 one year from now, 40000 two years from now.\"\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I do not agree with the post by @ElectricPavlov - neither with their conception, nor with their calculations.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Below I present my conception, my calculations and my solution, with the answer.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;After my solution, I presented the @ElectricPavlov writing with my comments.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "                      S O L U T I O N \r\n" );
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document.write( "**1.1. Timeline**\r\n" );
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document.write( "Here's a simple representation of the timeline:\r\n" );
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document.write( "    0 months:** Loan Disbursement\r\n" );
document.write( "    6 months:** Payment of R10,000 due (missed)\r\n" );
document.write( "   12 months:** Payment of R20,000 due (missed)\r\n" );
document.write( "   18 months:** Down payment of R50,000 made\r\n" );
document.write( "   24 months:** Payment of R40,000 due, and the farmer makes his last payment to settle his debt.\r\n" );
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document.write( "**1.2. Single Payment Calculation**\r\n" );
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document.write( "(a)  His accumulated debt \"after 18 months from now\" is \r\n" );
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document.write( "         base           the interest                base            the interest\r\n" );
document.write( "        scheduled         accrued                 scheduled           accrued\r\n" );
document.write( "         payment      for not paid amount          payment        for not paid amount\r\n" );
document.write( "        not paid     \"after 18 months from now\"   not paid      \"after 18 months from now\"\r\n" );
document.write( "        at the time   18-6 = 12 months overdue    at the time   18-12 = 6 months overdue\r\n" );
document.write( "                       against the schedule                       against the schedule\r\n" );
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document.write( "        10000     +   10000*(18-6)*(0.17/12)     +  20000     +  20000*(18-12)*(0.17/12) = 33400.\r\n" );
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document.write( "(b)  The balance \"at 18 months from now\" after paying 50000 against the loan is\r\n" );
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document.write( "         33400 - 50000 = -16600,  so the farmer is now ahead of his schedule.\r\n" );
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document.write( "                  (!)  Now THE BANK owes 16600 to the farmer.\r\n" );
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document.write( "      The problem does not describe what the bank does in this situation.\r\n" );
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document.write( "                  So, at this point I should stop in bewilderment  (formally).\r\n" );
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document.write( "      OK, let's assume that the bank makes nothing, so the farmer's money (16600) lie \r\n" );
document.write( "      and wait \"to 24 months from now\" with no change.\r\n" );
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document.write( "(c)  Then the single payment \"24 months from now\" is 40000 - 16600 = 23400.    <U>ANSWER</U>\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "=======================\r<BR>\n" );
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document.write( "Below I placed the tutor's @ElectricPavlov calculations with my comments.\r<BR>\n" );
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document.write( "To calculate the single payment Mr. Farmer needs to make in two years (24 months) from now to settle his debt, we need to consider the following:\r\n" );
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document.write( "* **Accumulated debt at 18 months:** This includes the missed payments, interest on those missed payments, and the remaining loan balance after the R50,000 down payment.\r\n" );
document.write( "* **Future value of the accumulated debt at 24 months:** We need to factor in the interest that will accrue on the accumulated debt over the additional 6 months.\r\n" );
document.write( "* **Future value of the R40,000 payment at 36 months:** The R40,000 payment is also due in two years, so we need to calculate its future value considering the interest.\r\n" );
document.write( "* **Single payment:** The sum of the future value of the accumulated debt and the future value of the R40,000 payment will be the total amount Mr. Farmer needs to pay.\r\n" );
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document.write( "**Calculations:**\r\n" );
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document.write( "* **Payment 1 Interest:** 10,000 Rand * (17% interest rate) * (18 months / 12 months) = 2,550 Rand\r\n" );
document.write( "                                                               why 18 months here? - should be 12 months overdue.  The number of 2,550 is wrong.\r\n" );
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document.write( "* **Payment 2 Interest:** 20,000 Rand * (17% interest rate) * (12 months / 12 months) = 3,400 Rand\r\n" );
document.write( "                                                               why 12 months here? - should be 6 months overdue.  The number of 3,400 is wrong.\r\n" );
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document.write( "* **Accumulated debt at 18 months:** 10,000 Rand (original payment) + 2,550 Rand (interest on payment 1) + 20,000 Rand (original payment 2) + 3,400 Rand (interest on payment 2) - 50,000 \r\n" );
document.write( "                                                               from what precedes, these numbers are wrong\r\n" );
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document.write( "Rand (down payment) = -14,050 Rand (negative value indicates Mr. Farmer still owes money)\r\n" );
document.write( "* **Future value of accumulated debt at 36 months:** -14,050 Rand * (1 + 17% interest rate * (18 months / 12 months)) = -17,632.75 Rand\r\n" );
document.write( "                                                     wrong interpretation: mr farmer is AHEAD of the schedule - so, the BANK owes money to mr. farmer.\r\n" );
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document.write( "* **Future value of R40,000 payment at 36 months:** 40,000 Rand * (1 + 17% interest rate * (12 months / 12 months)) = 46,800.00 Rand\r\n" );
document.write( "                                                      Why 12 months interest is calculated and added ? - It is wrong.\r\n" );
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document.write( "* **Single payment due at 36 months:** -17,632.75 Rand + 46,800.00 Rand = 29,167.25 Rand\r\n" );
document.write( "                                                       The calculations are incorrect and the answer is wrong.\r\n" );
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document.write( "**Therefore:**\r\n" );
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document.write( "Mr. Farmer needs to make a single payment of **R29,167.25** in two years (36 months) to settle his debt. This amount considers the accumulated debt, interest on missed payments, and the future value of the R40,000 payment due at that time.\r\n" );
document.write( "                                                This answer is wrong.\r\n" );
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document.write( "The calculations in the post by @ElectricPavlov are not consistent and contradict to their TimeLine.\r<BR>\n" );
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document.write( "As I see from this post, the other tutor (which is an AI, I believe) is not able to establish <BR>\n" );
document.write( "right strategy of solution and is not able to produce calculations correctly.\r<BR>\n" );
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document.write( "It works following the principle \"to generate as many words as possible, hoping that<BR>\n" );
document.write( "nobody will even try to figure out if it is correct\".\r<BR>\n" );
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