document.write( "Question 1142108: A man is planning to retire in 25 years. He
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Algebra.Com's Answer #762798 by ikleyn(52776) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "I will assume that the person deposits a regular amount at the end of every quarter during 25 years \r
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document.write( "    Different schemes are possible, and each such a scheme requires a separate consideration - but what I propose \r\n" );
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document.write( "    is natural and reasonable, making the problem correctly and precisely formulated.\r\n" );
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\n" ); document.write( "\n" ); document.write( " I will solve this problem in two steps.\r
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document.write( "First, I will determine how much money X should be accumulated on the account during 25 years,\r\n" );
document.write( "in order for to have enough to withdraw $32000 at the beginning of each of the next 10 years.\r\n" );
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document.write( "By withdrawing $32000 at the beginning of each year, the account (the remaining money) still earns 8% per annum compounded quarterly.\r\n" );
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document.write( "It means that effective annual rate for this account is   = 1.082432 compounded annually.\r\n" );
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document.write( "So, when you withdraw money during 10 years from your account, it still earns with effective rate of 1.082432 per year compounded annually.\r\n" );
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document.write( "Thus, it works as if it would be compounded annually at the rate of 8.2432%.\r\n" );
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document.write( "Such scheme withdrawing money was considered at the lesson  \r\n" );
document.write( "    Withdrawing a certain amount of money periodically from a compounded saving account  \r\n" );
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document.write( "The formula for the account value before it starts discharging is\r\n" );
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document.write( "    M = ,     (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( "    M  = 212387 dollars.\r\n" );
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document.write( "Now I am in position to determine how much the person should deposit each quarter during 25 years \r\n" );
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document.write( "to accumulate  212387 dollars in his account. The number of quarter periods is 25*4 = 100.\r\n" );
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document.write( "Now we have a standard Annuity saving plan, and the formula is\r\n" );
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document.write( "    212387 = ,     (2)\r\n" );
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document.write( "where D is the quarterly deposit amount.\r\n" );
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document.write( "The multiplier    is equal  312.2323 ,  \r\n" );
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document.write( "which implies from equation (2)  that  D =  = 680.22.\r\n" );
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document.write( "It is your answer:  During 25 years the person should deposit $680.22 at the end of each quarter to his account,\r\n" );
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document.write( "                    in order to withdraw  $32000  at the beginning of each year during 10 years at given conditions.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In this site, there is a group of lessons associated with annuity saving plans and retirement plans. They are\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
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\n" ); document.write( "\n" ); document.write( "From these lessons, you can learn the subject and can see many similar solved problems.\r
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