document.write( "Question 1151386: Belle, who has just started her first full-time salary job is determined to have $1 million in her account by the time she retires. She is now 25 and hopes to retire at 65 years of age. Her investments have been earning 6.25% annual return and she thinks it’s realistic that can be maintained.
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\n" ); document.write( "How much would Belle have to put aside each month, in order to reach her goal? [I solved and the answer is 469.06)\r
\n" ); document.write( "\n" ); document.write( "What is the total amount of money she will have saved? [2]\r
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Algebra.Com's Answer #773135 by ikleyn(52818)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            As the problem is worded,  printed,  posted and presented,  it is not complete and,  therefore,  is not fully accurate.\r
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\n" ); document.write( "\n" ); document.write( "            To be accurate,  it should say that \r
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\n" ); document.write( "\n" ); document.write( "                 a)   the account is compound;\r
\n" ); document.write( "\n" ); document.write( "                 b)   it should say what is the compound period,   and\r
\n" ); document.write( "\n" ); document.write( "                 c)   does she pay at the beginning or at the end of the compound period.\r
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\n" ); document.write( "\n" ); document.write( "            So,  I will assume that the account is compound;  the compound period is  1  month,  and she pays at the end of each month.\r
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document.write( "Then 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, 40, 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 = 0.0625/12;  n = 40*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 = \"1000000%2A%28%28%280.0625%2F12%29%29%2F%28%281%2B0.0625%2F12%29%5E%2840%2A12%29-1%29%29\" = $469.07.\r\n" );
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document.write( "Answer.  The necessary monthly deposit value is $469.07.\r\n" );
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document.write( "Note that of projected $1,000,000 the total of her deposits will be only  40*12 times $469.07, \r\n" );
document.write( "i.e. 40*12*469.07 = 225,153.60 dollars. The rest is what the account will earn/accumulate in 40 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
\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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