document.write( "Question 1193455: Julita owes Jose the following amounts:
\n" ); document.write( "a. 55,000 at the end of 4 years,
\n" ); document.write( "b. 48,000 at the end of 5 years, and
\n" ); document.write( "c. 75,000 due in 3 years from today at 9% converted quarterly.
\n" ); document.write( "What single payment at the end of 2 years will settle Julita’s
\n" ); document.write( "obligations if money is worth 15% converted monthly? \n" ); document.write( "

Algebra.Com's Answer #848711 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Julita owes Jose the following amounts:
\n" ); document.write( "a. 55,000 at the end of 4 years,
\n" ); document.write( "b. 48,000 at the end of 5 years, and
\n" ); document.write( "c. 75,000 due in 3 years from today at 9% $\"highlight%28cross%28converted%29%29\"$ compounded quarterly.
\n" ); document.write( "What single payment at the end of 2 years will settle Julita’s
\n" ); document.write( "obligations if money is worth 15% $\"highlight%28cross%28converted%29%29\"$ compounded monthly?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Calculations in the post by @yurtman all are incorrect.\r
\n" ); document.write( "\n" ); document.write( "        They are incorrect technically, since he uses incorrect effective growth factors everywhere.\r
\n" ); document.write( "\n" ); document.write( "        They are incorrect conceptually, since his solution is conceptually incorrect.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        In this problem, as it is worded, 15% compounded monthly is irrelevant data,
\n" ); document.write( "        which should not be used in the solution.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Regarding the problem itself, as worded in the post, it is soup of words with no sense.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To make sense from nonsense, the problem should be re-written/re-formulated this way:\r
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\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    Julita owes Jose the following amounts:\r\n" );
document.write( "      (a) 55,000 at the end of 4 years,\r\n" );
document.write( "      (b) 48,000 at the end of 5 years, and\r\n" );
document.write( "      (c) 75,000 at the end of 3 years. \r\n" );
document.write( "    Jose has an account in the bank, which pays 9% annually compounded quarterly.\r\n" );
document.write( "    Therefore, Jose agrees to accept a single payment from Julita at the end of 2 years\r\n" );
document.write( "    to deposit it to this account and to settle Julita's obligations this way.\r\n" );
document.write( "    What amount should pay Julita to Jose in 2 years from now ?\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution to this re-formulated problem.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "In this problem, we should calculate the value of the debt at the end of the two years from today.\r\n" );
document.write( "It is all what should be calculated, since this value represents the obligation at the end of 2 years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1. Calculate the value of each obligation at the end of 2 years from now:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Obligation 1 at the end of 2 years from now (rewind two years back from 4 years)\r\n" );
document.write( "      Value = 55000 / (1 + 0.09/4)^(2*4) \r\n" );
document.write( "      Value = 46031.61\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Obligation 2 at the end of 2 years from now (rewind three years back from 5 years)\r\n" );
document.write( "      Value = 48000 / (1 + 0.09/4)^(3*4)  \r\n" );
document.write( "      Value = 36752.04\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Obligation 3  at the end of 2 years from now (rewind one year back from 3 years)\r\n" );
document.write( "      Value = 75,000 / (1 + 0.09/4)^(1*4)\r\n" );
document.write( "      Value = 68613.25\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2. Calculate the Total of All Obligations two years from now\r\n" );
document.write( "\r\n" );
document.write( "     Total of the three obligations:  46031.61 + 36752.04 + 68613.25 = 151396.90\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The single payment of 151396.90 will settle Julita's obligations at the end of 2 years from now.   \r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Regarding the post by @yourtman (which is an AI, I believe), I see that it/he is not able to establish
\n" ); document.write( "right strategy of solution and is not able to produce calculations correctly.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It works following the principle \"to generate as many words as possible, hoping that
\n" ); document.write( "nobody will even try to figure out if it is correct\".\r
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\n" ); document.write( "\n" ); document.write( "

To the managers of this project

\r
\n" ); document.write( "\n" ); document.write( "On your side, you have a person - the problem's composer/creator - who produces
\n" ); document.write( "half-non-sensical writing and disseminate it in the Internet.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This person definitely does not understand what he writes.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Take all necessary measures to keep the project in order.\r
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\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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