document.write( "Question 1183073: Mr Hammond is 45 years of age and has a life expectancy of 10 more years. He
\n" ); document.write( "wishes to invest $20,000 in an annuity that will make a level payment at the end of
\n" ); document.write( "each year until his death. If the interest rate is 8%, what income can Mr Hammond
\n" ); document.write( "expect to receive each year? \n" ); document.write( "

Algebra.Com's Answer #813224 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            I will solve the problem under the assumption that Mr. Hammond withdraws a level payment
\n" ); document.write( "            at the beginning of each year to provide the money for living this year.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            It looks like much more realistic scenario, and it is usual assumption in this class of problems.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Use the general formula  A = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In this formula,  A is the deposited value ($20,000 in this case);  \r\n" );
document.write( "\r\n" );
document.write( "                  W  is the withdrawal annual rate W (the unknown value in this problem);  \r\n" );
document.write( "\r\n" );
document.write( "                  the annual compounding rate is  r = 0.08;  p = 1 + r = 1 + 0.08 = 1.08;   \r\n" );
document.write( "\r\n" );
document.write( "                  n is the number of payment periods  n= 10. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the formula\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          W =  =  = 2759.80 dollars.                 ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, the TOTAL amount obtained from the account (2759.80 each year) during 10 years is  2759.80*10 = 27,598 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The difference  $27,598 - $20000 = $7.598  is the INTEREST earned by the account during 10 years.   \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The uniform level withdrawal is $2759.80 per year.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "See my lessons in this site associated with annuity saving plans and retirement plans \r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "and especially lesson marked (*) in the list as the most relevant to the given problem.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "//////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The difference in answers between my post and the post by tutor @MathTherapy is due \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to the fact that we solved the problem under DIFFERENT ASSUMPTIONS.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );