document.write( "Question 1125957: How much money should be deposited into an account that earns 4.6% interest,compounded every month,so that after 20 years there is a balance of $24,000? \n" ); document.write( "
Algebra.Com's Answer #742294 by ikleyn(52788)\"\" \"About 
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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 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 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 = $24,000;  r = 0.046/12;  n = 20*12.  So, according to the formula (1), you get for the monthly payment \r\n" );
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document.write( "    P = \"24000%2A%28%28%280.046%2F12%29%29%2F%28%281%2B0.046%2F12%29%5E%2820%2A12%29-1%29%29%29\" = $61.14.\r\n" );
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document.write( "Answer.  The necessary monthly deposit value is $61.14.\r\n" );
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document.write( "Note that of projected $24,000 the total of deposits will be only  20*12 times $61.14, i.e. 20*12*61.14 = 14673.60 dollars.\r\n" );
document.write( "The rest is what the account will earn/accumulate in 20 years.\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
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