document.write( "Question 1135731: You want to be able to withdraw $45,000 from your account each year for 25 years after you retire. \r
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\n" ); document.write( "\n" ); document.write( "If your account earns 9% interest, how much will you need to deposit each year until retirement to achieve your retirement goals? \n" ); document.write( "
Algebra.Com's Answer #753392 by ikleyn(52862)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "    You want to be able to withdraw $45,000 from your account at the beginning of each year for 25 years after you retire. \r\n" );
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document.write( "    You expect to retire in 30 years. \r\n" );
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document.write( "    If your account earns 9% interest compounded yearly, how much will you need to deposit at the end of each year \r\n" );
document.write( "    until retirement to achieve your retirement goals?\r\n" );
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\n" ); document.write( "\n" ); document.write( "The solution is in 2 steps.\r
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\n" ); document.write( "\n" ); document.write( "Step 1\r
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document.write( "Step 1 is to determine what amount you need to have at your account after 30 years depositing to it\r\n" );
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document.write( "in order for to be able to withdraw $45,000 from your account at the beginning of each year for 25 years after you retire.\r\n" );
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document.write( "The general formula to calculate this amount is  \r\n" );
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document.write( "    X = \"W%2Ap%2A%28%281-p%5E%28-n%29%29%2Fr%29\".\r\n" );
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document.write( "In this case  the withdrawal semi-annual rate is W = $45000,  the annual compounding rate \r\n" );
document.write( "is  r = 0.09,  p = 1 + 0.09 = 1.09, the number of payment periods  is n = 25. So\r\n" );
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document.write( "    X = \"45000%2A1.09%2A%28%281-1.09%5E%28-25%29%29%2F0.09%29\" = 481,797.53 dollars.     \r\n" );
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document.write( "At this step we determine how big the annual deposit should be to provide this amount of $481,797.53 after 30 years of depositing.\r\n" );
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document.write( "This time it is 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 annual payment (deposit); r is the annual percentage yield presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of years, in this case).\r\n" );
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document.write( "From this formula, you get for the annual 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 = $481,797.53;  r = 0.09;  n = 30.  So, according to the formula (1), you get for the annual payment \r\n" );
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document.write( "    P = \"481797.53+%2A%280.09%2F%28%281%2B0.09%29%5E30-1%29%29\" = $3534.64.\r\n" );
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document.write( "So, your annual deposit should be  $3534.64.     ANSWER\r\n" );
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document.write( "ANSWER.  To provide your goal, you need to deposit  $3534.64 dollars annually at the end of each year during 30 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to learn the theory of this financing and/or see other similar solved problems,  look into my lessons in this site\r
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\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Annuity Due 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( "    - Withdrawing a certain amount of money periodically from a compounded saving account \r
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