document.write( "Question 1174080: You want to be able to withdraw $20,000 from your account each year for 20 years after you retire.\r
\n" ); document.write( "\n" ); document.write( "You expect to retire in 25 years.\r
\n" ); document.write( "\n" ); document.write( "If your account earns 5% interest, how much will you need to deposit each year until retirement to achieve your retirement goals? \n" ); document.write( "

Algebra.Com's Answer #799451 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "You want to be able to withdraw $20,000 from your account each year for 20 years after you retire.\r
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\n" ); document.write( "\n" ); document.write( "If your account earns 5% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?
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\n" ); document.write( "\n" ); document.write( "Step 1.\r
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document.write( "First, I will determine how much money X should be accumulated on the account during 25 years to the time  of retiring,\r\n" );
document.write( "in order for to have enough to withdraw $20000 at the beginning of each year for 20 years.\r\n" );
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document.write( "By withdrawing $20000 each year, my compound account (the remaining money) still earns 5% per annum,  so everything works as it was \r\n" );
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document.write( "considered/described at the lesson  Withdrawing a certain amount of money periodically from a compounded saving account  in this site.\r\n" );
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document.write( "Thus the formula for the account value before it starts recharging is\r\n" );
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document.write( "    X = ,     (1)\r\n" );
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document.write( "which gives us the value at the account of\r\n" );
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document.write( "    X  = 249244.21 dollars.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Step 2. \r
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document.write( "Now I am in position to determine how much I should deposit at the end of each year during 25 years to the starting moment of the retiring\r\n" );
document.write( "to accumulate  249244.21 dollars in my account. \r\n" );
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document.write( "It is the standard Annuity saving plan, and the formula is\r\n" );
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document.write( "    249244.21 = ,     (2)\r\n" );
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document.write( "where D is the annual deposit amount.\r\n" );
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document.write( "The multiplier   = 47.7271,\r\n" );
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document.write( "which implies from equation (2)  that  D =  = 5222.28  dollars.\r\n" );
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document.write( "It is your answer:  During 25 years, you should deposit $5222.28 at the end of each year to your account,\r\n" );
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document.write( "                    in order for to withdraw $20000 annually from yours account for 20 years after your retiring.\r\n" );
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\n" ); document.write( "\n" ); document.write( "My lessons in this site associated with annuity saving plans and retirement plans are \r
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\n" ); document.write( "\n" ); document.write( "    - Geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for geometric progressions \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
\n" ); document.write( "\n" ); document.write( "    - Miscellaneous problems on retirement plans \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Geometric progressions\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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