Algebra.Com's Answer #845522 by ikleyn(52909)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Joshua deposited $3560.00 at the beginning of every 6 months for 11 years into a fund
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document.write( "paying 3.5% compounded semi-annually. Fourteen years after the first deposit,
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document.write( "he then converted the existing balance into an annuity due paying him equal annual payments
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document.write( "for 22 years. If interest for the annuity due is 5% compounded annually,
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document.write( "what is the size of the annual payment?
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document.write( "First 11 years, the account accumulates money as annuity-due saving plan, which is deposited\r\n" );
document.write( "$3560 at the beginning of each 6 months.\r\n" );
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document.write( "Use the standard formula for the future value at the end of this 11-years time period\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 the semi-annual payment (deposit) \r\n" );
document.write( "at the beginning of each payment period; r is the semi-annual effective percentage \r\n" );
document.write( "yield presented as a decimal; n is the number of deposits (= the number of years \r\n" );
document.write( "multiplied by 2, or n= 11*2 = 22, in this case).\r\n" );
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document.write( "Under the given conditions, P = 3560; r = 0.035/2; n = 11*4 = 44. \r\n" );
document.write( "So, according to the formula (1), the future value in 11 years is\r\n" );
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document.write( " FV =  = $96193.53 (rounded). (2)\r\n" );
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document.write( "Two years after that, on years 12 and 13, the deposits were stopped;\r\n" );
document.write( "but the amount is still compounded semi-annually; so, at the end of the 13-th year,\r\n" );
document.write( "there ae  = 103105.90 dollars on the account.\r\n" );
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document.write( " Now the account is converted and works as the sinking fund, \r\n" );
document.write( " paying out for 22 years at the beginning of each year.\r\n" );
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document.write( "The formula connecting starting amount of $103105.90 and the annual payouts W is\r\n" );
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document.write( " 103105.90 =  . (3)\r\n" );
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document.write( "In this formula, calculate the factor separately\r\n" );
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document.write( "  = 13.82115271. (4)\r\n" );
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document.write( "Now from equation (3),\r\n" );
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document.write( " W =  = 7460 dollars.\r\n" );
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document.write( "At this point, the solution is complete and the answer is obtained.\r\n" );
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document.write( "ANSWER. The size of the annual payment is 7460 dollars.\r\n" );
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document.write( "Solved.\r
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document.write( "---------------\r
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document.write( "On annuity saving plans and sinking funds, see my lessons in this site \r
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document.write( " - Ordinary Annuity saving plans and geometric progressions\r
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document.write( " - Annuity Due saving plans and geometric progressions\r
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document.write( " - Solved problems on Ordinary Annuity saving plans \r
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document.write( " - Finding present value of an annuity, or an equivalent amount in today's dollars \r
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document.write( " - Withdrawing a certain amount of money periodically from a compounded saving account\r
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document.write( "From this lessons, learn the subject once and for all.\r
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