document.write( "Question 1207417: An investment fund that pays quarterly dividends for 10 years yields an annual return of 6.6%. If the initial price of the fund is $200, what is the amount of the dividend? \n" ); document.write( "

Algebra.Com's Answer #845465 by ikleyn(53763) $\"\"$ $\"About$

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\n" ); document.write( "An investment fund that pays quarterly dividends for 10 years yields an annual return of 6.6%.
\n" ); document.write( "If the initial price of the fund is $200, what is the amount of the dividend?
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document.write( "This investment fund, in other terms, is a sinking fund, which provides regular payouts\r\n" );
document.write( "quarterly and is compounded quarterly at the nominal compounding rate of 6.6% per year.\r\n" );
document.write( "The fund works in this mode during 10 years. After 10 years, the fund is empty.\r\n" );
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document.write( "The problem's formulation is INCOMPLETE, since it does not say if the fund makes payments\r\n" );
document.write( "at the end or at the beginning of each quarter. The formulas to calculate future values\r\n" );
document.write( "of such sinking fund are DIFFERENT in these cases. In my solution below, I will assume\r\n" );
document.write( "that the payments are at the end of each quarter.\r\n" );
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document.write( "For such sinking fund, the formula which connects the starting amount X and the quarterly \r\n" );
document.write( "payment Q is \r\n" );
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document.write( "    X = .    (1)\r\n" );
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document.write( "In this formula, Q is  the regular withdrawal per quarter;  the factual quarterly compounding rate \r\n" );
document.write( "is  r = ,  p = , and the number of payment periods  is n = 10 years * 4 quarters = 40. So\r\n" );
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document.write( "    200 = .    (2)\r\n" );
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document.write( "The unknown is the value of quarterly payments Q.\r\n" );
document.write( "In this formula, we can calculate the factor (multiplier)\r\n" );
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document.write( "     = 29.11257449.\r\n" );
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document.write( "Then  from formula (2)  Q =  = 6.869883668.\r\n" );
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document.write( "We round it to the closest cent and get the\r\n" );
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document.write( "ANSWER.  The quarterly payment out is 6.87 dollars.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see other similar (and different) solved problems on regular withdrawing from sinking fund
\n" ); document.write( "compounded periodically, look into the lesson\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( "From this lesson, learn the subject once and for all.\r
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