document.write( "Question 1204181: Andrea, a self-employed individual, wishes to accumulate a retirement fund of $200,000. How much should she deposit each month into her retirement account, which pays interest at a rate of 5.5%/year compounded monthly, to reach her goal upon retirement 25 years from now? (Round your answer to the nearest cent.) \n" ); document.write( "
Algebra.Com's Answer #840260 by ikleyn(52834)\"\" \"About 
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\n" ); document.write( "Andrea, a self-employed individual, wishes to accumulate a retirement fund of $200,000.
\n" ); document.write( "How much should she deposit each month into her retirement account, which pays interest
\n" ); document.write( "at a rate of 5.5%/year compounded monthly, to reach her goal upon retirement 25 years from now?
\n" ); document.write( "(Round your answer to the nearest cent.)
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\n" ); document.write( "\n" ); document.write( "        This problem is posed incorrectly. To be correct, the problem must to point WHEN the deposits
\n" ); document.write( "        are made, at the end or at the beginning of each compounding period (which is month).
\n" ); document.write( "        Usually/traditionally, in such problems it is assumed that the deposit are made at the end of each month,
\n" ); document.write( "        so I will follow this hypothesis. But I should notice, with the DEEP SORROW, that the creators
\n" ); document.write( "        of this problems do not know the basics of the subject and are not able to pose the problem in a right way.\r
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document.write( "It is a classic Ordinary Annuity saving plan. The general formula is \r\n" );
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document.write( "    FV = \"P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29\",    \r\n" );
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document.write( "where  FV is the future value of the account;  P is the monthly payment (deposit); r is the monthly percentage yield \r\n" );
document.write( "presented as a decimal; n is the number of deposits (= the number of years multiplied by 12, in this case).\r\n" );
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document.write( "From this formula, you get for the monthly payment \r\n" );
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document.write( "    P = \"FV%2A%28r%2F%28%281%2Br%29%5En-1%29%29\".     (1)\r\n" );
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document.write( "Under the given conditions, FV = $200,000;  r = 0.055/12;  n = 25*12.  So, according to the formula (1), you get \r\n" );
document.write( "for the monthly payment \r\n" );
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document.write( "    P = \"200000%2A%28%28%280.055%2F12%29%29%2F%28%281%2B0.055%2F12%29%5E%2825%2A12%29-1%29%29\" = $311.51.\r\n" );
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document.write( "Answer.  The necessary monthly deposit value is $311.51.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On Ordinary Annuity saving plans,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Ordinary Annuity saving plans\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.\r
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\n" ); document.write( "\n" ); document.write( "When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.\r
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\n" ); document.write( "\n" ); document.write( "To make such complicated calculations as they are in this problem,
\n" ); document.write( "you should have/use an appropriate calculator for such long formulas.\r
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\n" ); document.write( "\n" ); document.write( "Ideal choice is MS Excel, if you have it in your computer.\r
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\n" ); document.write( "\n" ); document.write( "Then you write a formula in a text editor, copy-paste it
\n" ); document.write( "into an Excel work-sheet cell and click \"enter\" - the result is ready
\n" ); document.write( "in the next second.\r
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\n" ); document.write( "\n" ); document.write( "If you have no MS Excel in your computer, you may find similar
\n" ); document.write( "free of charge calculators in the Internet. One such calculator is\r
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\n" ); document.write( "\n" ); document.write( "www.desmos.com/calculator\r
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\n" ); document.write( "\n" ); document.write( "It allows you to do the same thing: you write a formula in a text editor,
\n" ); document.write( "copy-paste it into this calculator and click \"enter\" - the result is ready
\n" ); document.write( "in the next second.\r
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