document.write( "Question 1185955: Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period.\r
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Algebra.Com's Answer #816925 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the payment that should be used for the annuity due whose future value is given.
\n" ); document.write( "Assume that the compounding period is the same as the payment period.
\n" ); document.write( "$20,000; quarterly payments for 17 years; interest rate 5% the payment should be?
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\n" ); document.write( "\n" ); document.write( "            What @Theo calculated for you, was the Ordinary Annuity saving plan, when the regular deposits are made at the END of each quarter.\r
\n" ); document.write( "\n" ); document.write( "            The given problem asks about the Annuity Due saving plan, when the regular deposits are made AT THE BEGINNING of each quarter.\r
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\n" ); document.write( "\n" ); document.write( "            So, @Theo's calculations are not appropriate for this problem.\r
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\n" ); document.write( "\n" ); document.write( "            THEREFORE, I came to bring you a correct solution.\r
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document.write( "It is a classic Annuity Due saving plan. The general formula is \r\n" );
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document.write( "    FV = ,    (1)\r\n" );
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document.write( "where  FV is the future value of the account;  P is your quarterly payment (deposit), which is made at the beginning of each quarter; \r\n" );
document.write( "r is the effective quarterly percentage yield presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of years multiplied by 4, in this case).\r\n" );
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document.write( "Under the given conditions, FV = 20000;  r = 0.05/4;  n = 17*4 = 68.  So, according to the formula (1), the quarterly payment should be\r\n" );
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document.write( "    P =  =  $186.02.    ANSWER\r\n" );
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document.write( "Note that you deposit only  17*4*$186.02 = $12,649.36.  The rest is what the account earns/accumulates in 17 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On Ordinary Annuity and Annuity Due saving plans, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity 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( "    - Solved problems on Ordinary Annuity saving plans \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.\r
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\n" ); document.write( "\n" ); document.write( "When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.\r
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