document.write( "Question 1206598: How much must be placed each month into a retirement account earning 12%compounded month if the value of the account is to rea h $1000000 in 20 years \n" ); document.write( "
Algebra.Com's Answer #844169 by ikleyn(52786)\"\" \"About 
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\n" ); document.write( "How much must be placed  at the end of  each month into a retirement account earning 12%
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\n" ); document.write( "\n" ); document.write( "        I edited your post to make it sensical.\r
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document.write( "This problem is to determine the amount of monthly payments/deposits.\r\n" );
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document.write( "Since the payments are at the end of each month, it is a classic Ordinary Annuity saving plan. \r\n" );
document.write( "The general formula to start (which is a PREREQUISITE and which you should know from your textbook) 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\n" );
document.write( "r is the monthly effective percentage yield presented as a decimal; \r\n" );
document.write( "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 = $1,000,000;  r = 0.12/12 = 0.01;  n = 20*12 = 240.  \r\n" );
document.write( "So, according to the formula (1), you get for the monthly payment \r\n" );
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document.write( "    P = \"1000000%2A%28%28%280.12%2F12%29%29%2F%28%281%2B0.12%2F12%29%5E%2820%2A12%29-1%29%29\" = \"1000000%2A%280.01%2F%281.01%5E240-1%29%29\" = $1010.87.\r\n" );
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document.write( "Answer.  The necessary monthly deposit is $1010.87.\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
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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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