document.write( "Question 1207426: What payment made at the end of each year for 18 years will amount to $16,000 at 4.2% compounded monthly?
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Algebra.Com's Answer #852184 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "What payment made at the end of each year for 18 years will amount to $16,000 at 4.2% compounded monthly?
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\n" ); document.write( "\n" ); document.write( "        In his post, tutor @Theo solved this problem using a calculator,\r
\n" ); document.write( "\n" ); document.write( "        and described a methodology solving this problem using calculator.\r
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\n" ); document.write( "\n" ); document.write( "        It is good, but since this website is intended to teach mathematical methods,\r
\n" ); document.write( "\n" ); document.write( "        I present here mathematical solution with all detailed explanations.\r
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document.write( "As it is given in the post, this annuity is not standard: the payments are made at the end of each year,\r\n" );
document.write( "while compounding is made at the end of each month.\r\n" );
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document.write( "Analytic formulas exist only for coinciding schedules of payments and compounding.\r\n" );
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document.write( "But we can use an equivalent standard synchronized scheme, considering payments at the end of each year \r\n" );
document.write( "and compounding at the end of each year with the   annual multiplicative growth rate  \r\n" );
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document.write( "    1+r =  = 1.042818007.    (1)\r\n" );
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document.write( "Now we can use a standard formula for such ordinary annuity \r\n" );
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document.write( "    FV = .    (2)\r\n" );
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document.write( "In this formula, FV is the future value in 18 years; P is the annual payment, the unknown value\r\n" );
document.write( "which we should find.\r\n" );
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document.write( "We calculate the factor in the formula (2) separately\r\n" );
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document.write( "     =  = 26.31908947.\r\n" );
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document.write( "Then from formula (2) we find\r\n" );
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document.write( "    P =  =  = 607.93 dollars.\r\n" );
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document.write( "Thus we found out the annual payment value. It is $607.93.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "My result is precisely consisted with the answer by @Theo.\r
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\n" ); document.write( "\n" ); document.write( "Now you can solve similar problems mathematically and check them using calculator.\r
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\n" ); document.write( "\n" ); document.write( "It is a good and reliable strategy.\r
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