document.write( "Question 1207349: Calculate the purchase price of an annuity paying $200 per month for 10 years with a lump payment of $2000 on the same day as the last payment of $200, at 6.5% compounded monthly. \n" ); document.write( "

Algebra.Com's Answer #845183 by ikleyn(52864) $\"\"$ $\"About$

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\n" ); document.write( "Calculate the purchase price of an annuity paying $200 per month for 10 years
\n" ); document.write( "with a lump payment of $2000 on the same day as the last payment of $200,
\n" ); document.write( "at 6.5% compounded monthly.
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\n" ); document.write( "\n" ); document.write( "        The problem does not say if the regular payments (withdrawals) are made at the beginning or at the end of each month.\r
\n" ); document.write( "\n" ); document.write( "        Also, from the problem, it is unclear if the lump payment of $2000 does include the last regular payment of $200 or is an addition to it.\r
\n" ); document.write( "\n" ); document.write( "        Due to this reason, the problem formulation is mathematically lame.\r
\n" ); document.write( "\n" ); document.write( "        In my solution below, I assume that the regular payments (withdrawals) are made at the end of each month.\r
\n" ); document.write( "\n" ); document.write( "        I also assume that the lump payment of $2000 is an addition to the last regular payment of $200.\r
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document.write( "The sough purchase price is the sum of two amounts.\r\n" );
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document.write( "First amount is the starting amount of an annuity that provides paying (from annuity to you) $200 per month for 10 years.\r\n" );
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document.write( "Second amount is the starting amount which provides a lump payment (from the annuity to you) of $2000 in 10 years from now.\r\n" );
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document.write( "To find first amount, use the formula  X = .\r\n" );
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document.write( "In this case,  W = $200 is the monthly withdrawal;  \r\n" );
document.write( "r is the effective monthly compounding rate  r = 0.065/12;  \r\n" );
document.write( "p = 1 + 0.065/12; \r\n" );
document.write( "n is the number of withdrawals (the same as the number of months, n = 10*12 = 120).\r\n" );
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document.write( "So, \r\n" );
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document.write( "    X =  = 17613.70 dollars for the first amount.\r\n" );
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document.write( "To find the value of the second amount, Y, use this equation\r\n" );
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document.write( "    2000 = .\r\n" );
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document.write( "From this equation,  Y =  = 1045.924586, or 1045.92 dollars (rounded).\r\n" );
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document.write( "Thus the  ANSWER  to the problem's question is this sum\r\n" );
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document.write( "    X + Y = 17613.70 + 1045.92 = 18659.62 dollars.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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