document.write( "Question 1142508: If Naomi decides that she will invest $4 comma 500 per year in a 4% annuity for the first ten years, $9,000 for the next ten years, and $13,500 for the next ten years, how much will she accumulate? Treat each ten-year period as a separate annuity. After the ten years of an annuity, then it will continue to grow at compound interest for the remaining years of the 30 years. \n" ); document.write( "

Algebra.Com's Answer #763214 by ikleyn(52776) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "The major idea of the solution is that the FUTURE VALUE of so organized saving plan is the sum of FUTURE VALUES of 3 (three) annuities.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "First annuity is 30 years ordinary annuity with the annual deposits of $4500 at 4% APY.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The second annuity is 20 years ordinary annuity with the annual deposits of $4500 at 4% APY.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And the third annuity is 10 years ordinary annuity with the annual deposits of $4500 at 4% APY.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The first annuity starts \"this\" year (or, better to say, it starts \"today\" with the first deposit at the end of \"this\"year); \r\n" );
document.write( "\r\n" );
document.write( "the second annuity starts 10 years after; and the third annuity starts 20 years after.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can EASILY understand why it is so, by splitting each $9000 deposits in two deposits by $4500 each: \r\n" );
document.write( "\r\n" );
document.write( "    - then you continue the first annuity with $4500 deposits every year from 11-th year till 20-th year,\r\n" );
document.write( "\r\n" );
document.write( "    - and you starts the second annuity with $4500 deposits annually from the year 11-th till 20-th.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And then splitting each $13500 deposits in three deposits by $4500 each:\r\n" );
document.write( "\r\n" );
document.write( "    - then you continue the first annuity with $4500 deposits every year from 21-th year till 30-th year inclusively,\r\n" );
document.write( "\r\n" );
document.write( "    - then you continue the second annuity with $4500 deposits every year from 21-th year till 30-th year inclusively,\r\n" );
document.write( "\r\n" );
document.write( "    - and you starts the third annuity with $4500 deposits annually from the year 21-th till 30-th inclusively.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the total future value after 30 years will be\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV = FV1 + FV2 + FV3,  where\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         FV1 = future value of the 4% annuity with $4500 deposits during 30 years;\r\n" );
document.write( "\r\n" );
document.write( "         FV2 = future value of the 4% annuity with $4500 deposits during 20 years;\r\n" );
document.write( "\r\n" );
document.write( "         FV3 = future value of the 4% annuity with $4500 deposits during 10 years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The rest is just a technique.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV1 =  =  = 252382.22;\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV2 =                  = 134001.36\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV3 =                  =  54027.75.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the answer is the sum   252382.22 + 134001.36 + 54027.75 = 440411.33 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  440411.33 dollars.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );