document.write( "Question 1173176: A person wants to buy life insurance policy which would yield a large enough sum of money to provide for 20 annual payments of $50000 to surviving members of the family.The payment should begin 1 year from the time of death.It is assumed that interest could earned on the sum received from the policy at the rate of 8% compounded annually.
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Algebra.Com's Answer #798446 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "A person wants to buy life insurance policy which would yield a large enough sum of money to provide for 20 annual payments
\n" ); document.write( "of $50000 to surviving members of the family. The payment should begin 1 year from the time of death. It is assumed that interest
\n" ); document.write( "could earned on the sum received from the policy at the rate of 8% compounded annually.
\n" ); document.write( "a) What amount of insurance should be taken out so as to insure the desired annuity?
\n" ); document.write( "b) How much interest will be earned on the policy benefits over the 20 year period?
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\n" ); document.write( "\n" ); document.write( "Let me re-formulate the problem to make it crystally clear.\r
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document.write( "    There is an account with starting amount X dollars; the value of X is unknown now.\r\n" );
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document.write( "    We want to withdraw $50000 from this account during 20 years, at the beginning of each year \r\n" );
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document.write( "    (starting 1 year after the death: so, if the person died 01/01/2030, for example, then the account starts working\r\n" );
document.write( "     on 01/01/2031 morning with the amount of X dollars, and first withdraw goes on 01/01/2031 afternoon - and then every year after that).\r\n" );
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document.write( "    The account is compounded annually at the annual rate of  8%  at Dec., 31.\r\n" );
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document.write( "    Find the starting value X at the account (at 01/01/2031), which provides uninterrupted functioning of the account during 20 years.\r\n" );
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document.write( "Use the general formula  X = \"W%2Ap%2A%28%281-p%5E%28-n%29%29%2Fr%29\".\r\n" );
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document.write( "In this formula,  W  the withdrawal annual rate W = $50000;  the annual compounding rate \r\n" );
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document.write( "is  r = 0.08;  p = 1 + r = 1 + 0.08 = 1.08;   n is the number of payment periods  n= 20. \r\n" );
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document.write( "From the formula\r\n" );
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document.write( "          X = \"50000%2A1.08%2A%28%281-1.08%5E%28-20%29%29%2F0.08%29\" = 530,180 dollars.                 ANSWER to question (a)\r\n" );
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document.write( "Next, the amount obtained from the account ($50000 each year) is  50000*20 = 1,000,000 dollars.\r\n" );
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document.write( "The difference  $1,000,000 - $530,180 = $469820  is the INTEREST earned by the account during 20 years.     ANSWER to question (b)\r\n" );
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document.write( "ANSWER.  To provide the  goal, the starting amount should be  $530180  at the account.\r\n" );
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document.write( "         The earned interest is $469820.\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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