document.write( "Question 1113633: Best Motors has hired Robert Trent as its new president. Terms included the company’s agreeing to pay retirement benefits of $17,900 at the end of each semiannual period for 12 years. This will begin in 4,015 days. If the money can be invested at 8% compounded semiannually, what must the company deposit today to fulfill its obligation to Robert? \n" ); document.write( "

Algebra.Com's Answer #728725 by ikleyn(52777) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "I will interpret the condition in this way:\r
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document.write( "    1)  We have first the period of    = 11 years,  when the initial deposit of X dollars grows at  8%  compounded semiannually.\r\n" );
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document.write( "    2)  Then the second period starts,  when the company withdraw  $17900 semiannually for  12 years to fulfill its obligation to Robert.\r\n" );
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document.write( "        During this period of  12 years the rest of the account is still compounded at  8% semiannually, \r\n" );
document.write( "        and at the end of the  12 years period the amount vanishes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The condition does not formulate all these details, so, from one side, it is my own interpretation / (fantasy).\r
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\n" ); document.write( "\n" ); document.write( "From the other side, only this interpretation makes the problem really interesting, and it is major reason, why I start to work on it.\r
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document.write( "1.  After 11 years, the initial deposit of X dollars becomes\r\n" );
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document.write( "    P =  = .\r\n" );
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document.write( "2.  Then the following next 12 years period we have the ordinary annuity plane with the NEGATIVE semiannual deposit (= withdraw) of $17900.\r\n" );
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document.write( "    So, the usual ORDINARY ANNUITY PLAN formula works with the negative deposit of 17900 dollars:\r\n" );
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document.write( "   \r\n" );
document.write( "    P =  = .\r\n" );
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document.write( "    So your equation to find X is THIS:\r\n" );
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document.write( "        = .\r\n" );
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document.write( "       x*2.369919 = 279502.6  =====>  X =  = 117937.60.\r\n" );
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document.write( "Answer.  Under the given condition and interpretation the initial deposit the company must make TODAY is  117937.60 dollars.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Ordinary Annuity saving plans and geometric progressions\r
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\n" ); document.write( "\n" ); document.write( "I absolutely agree with John in that you do not need copy your post many times - it only annoys/irritates the tutors and works against your best interests.\r
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