document.write( "Question 1176067: A state lotto has a prize that pays $1,700 each week for 40 years.\r
\n" ); document.write( "\n" ); document.write( "Find the total value of the prize: $
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\n" ); document.write( "\n" ); document.write( "If the state can earn 3% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments? \n" ); document.write( "

Algebra.Com's Answer #850588 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A state lotto has a prize that pays $1,700 each week for 40 years.\r
\n" ); document.write( "\n" ); document.write( "(a) Find the total value of the prize: $
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\n" ); document.write( "\n" ); document.write( "(b) If the state can earn 3% interest on investments, how much money will they need
\n" ); document.write( "to put into an account now to cover the weekly prize payments?
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\n" ); document.write( "\n" ); document.write( "        Calculations in the post by @CPhill are incorrect and inaccurate,\r
\n" ); document.write( "\n" ); document.write( "        as practically always in all his Finance calculations.\r
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\n" ); document.write( "\n" ); document.write( "        In this my post, I present my calculation, which gives different answer.\r
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document.write( "This problem is about the starting amount of a sinking fund, which pays out $1700\r\n" );
document.write( "each week during 40 years, compounding weekly at 3% annual interest.\r\n" );
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document.write( "The year is 365/7, or about 52 weeks, so I will use 52 weeks per year.\r\n" );
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document.write( "Use the formula for the monthly payment of a sinking fund\r\n" );
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document.write( "    IV = ,\r\n" );
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document.write( "where IV stands for the initial value, PMT is the annual outpayment value, \r\n" );
document.write( "r is the annual rate, n is the number of payment/compounding (52 times the number of years, in this problem).\r\n" );
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document.write( "With the given data, the formula for calculations is\r\n" );
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document.write( "    IV =  = 2,058,841  dollars.\r\n" );
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document.write( "At this point, I copy-paste this formula into an Excel spreadsheet\r\n" );
document.write( "without making intermadiate calculations.\r\n" );
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document.write( "Excel spreadsheet is a powerfull calculator. It keeps enough decimal places\r\n" );
document.write( "to provide the necessary precision.  The value, which I got this way is\r\n" );
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document.write( "           PV = 2,058,840.57.\r\n" );
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document.write( "ANSWER.  The initial/starting value of the fund is  about  $2,058,841.\r\n" );
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document.write( "         This amount is deposited initially, and it provides\r\n" );
document.write( "         no-failure payments of $1,700 at the end of each week during 40 years,\r\n" );
document.write( "         under given conditions.\r\n" );
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document.write( "         This initial/starting value of the fund is the \"present\" value of the prize, \r\n" );
document.write( "         which is won in the lottery.\r\n" );
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document.write( "         Notice that the total outpayment in 40 years, under the given condition, \r\n" );
document.write( "         is  40*52*1700 = 3,536,000.\r\n" );
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document.write( "         The difference $3,536,000 - $2,058,841 = $1,477,159  is the interest, which the fund earned in 40 years.\r\n" );
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The lesson to learn from this my post is two-fold

(1) In such Finance calculations, use powerful enough calculator to provide the necessary precision.\r
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\n" ); document.write( "\n" ); document.write( " (2) Do not make intermediate rounding ( ! ) Round only the final value ( ! )\r
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