document.write( "Question 1209861: How much would you need to deposit in an account each month in order to have $20,000 in the account in 6 years? Assume the account earns 4% annual interest, compounded monthly. (Enter your answer to 2 decimal places.)
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Algebra.Com's Answer #850904 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "How much would you need to deposit in an account each month in order to have $20,000 in the account in 6 years?
\n" ); document.write( "Assume the account earns 4% annual interest, compounded monthly. (Enter your answer to 2 decimal places.)
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document.write( "It is a classic Ordinary Annuity saving plan (assuming that the deposits are made at the end of each month). \r\n" );
document.write( "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\n" );
document.write( "r is the effective monthly compounding rate 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 = $20,000;  r = 0.04/12;  n = 6*12 = 72.  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 = \"20000%2A%28%28%280.04%2F12%29%29%2F%28%281%2B0.04%2F12%29%5E72-1%29%29\" = $246.24   (rounded).\r\n" );
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document.write( "Answer.  The necessary monthly deposit value is $246.24.\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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\n" ); document.write( "\n" ); document.write( "To make such complicated calculations as they are in this problem,
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\n" ); document.write( "\n" ); document.write( "Ideal choice is MS Excel, or Google spreadsheets, 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
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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 online 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
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