document.write( "Question 1151380: Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselves the whole amount at the beginning of each year, they have decided that payment at the beginning of each quarter of $12,000 gives them the right balance of flexibility and maximized interest earnings. They feel they can safely earn an interest rate of 8%, compounded quarterly, on their money and they are budgeting based on the prediction that they will live until they are 90 years old. \r
\n" ); document.write( "\n" ); document.write( "How much money will they have to have saved by the time they are 60 in order to reach their retirement goal? [1]\r
\n" ); document.write( "\n" ); document.write( "If the same total calculated above was to be saved, but no interest earned whatsoever, how much would be available to live on each quarter? [2]\r
\n" ); document.write( "\n" ); document.write( "If the full 30 years are lived and quarterly budget spent, how much money in total will have been utilized in retirement? [3]\r
\n" ); document.write( "\n" ); document.write( "How much will have been earned in interest? [4] \n" ); document.write( "

Algebra.Com's Answer #773128 by ikleyn(52879) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "It works in this way:  they withdraw $12000 at the beginning of every quarter, and the account is compounded quarterly \r\n" );
document.write( "at the nominal rate of 8% per year.\r\n" );
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document.write( "The general formula  to calculate the starting amount at the account is\r\n" );
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document.write( "    X = .\r\n" );
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document.write( "In this formula, W is  the regular withdrawal per quarter, W = $12000;  the factual quarterly compounding rate \r\n" );
document.write( "is  r = 0.08/4 = 0.02,  p = 1 + 0.02 = 1.02, and the number of payment periods  is n = 30 years * 4 quarters = 120. So\r\n" );
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document.write( "          X =  = 555,149.96 dollars.     It is the  ANSWER  to the problem's question [1].\r\n" );
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document.write( "The answer to question [2] is   = 0.39 dollars.\r\n" );
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document.write( "The answer to question [3] is 30*4*12000 = 1,440,000 dollars.\r\n" );
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document.write( "Regarding question [4], I do not understand precisely its meaning.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See my lessons in this site associated with annuity saving plans and retirement plans \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( "and especially lesson marked (*) in the list as the most relevant to the given problem.\r
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