document.write( "Question 1205773: Mr. Thompson wants to make monthly deposits into an annuity for his child so that $10,000 will be available in 8 years. If the interest rate is 8% compounded monthly, find the full deposit. \n" ); document.write( "
Algebra.Com's Answer #842797 by ikleyn(52782)\"\" \"About 
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\n" ); document.write( "Mr. Thompson wants to make monthly deposits into an annuity for his child
\n" ); document.write( "so that $10,000 will be available in 8 years.
\n" ); document.write( "If the interest rate is 8% compounded monthly, find the full deposit.
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document.write( "If the monthly deposits are made at the end of each month, then it is a classic \r\n" );
document.write( "Ordinary Annuity saving plan. The general formula is \r\n" );
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document.write( "    FV = \"P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29\",    \r\n" );
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document.write( "where  FV is the future value of the account;  P is the monthly payment (deposit); \r\n" );
document.write( "r is the monthly percentage yield presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of years multiplied by 12, in this case).\r\n" );
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document.write( "From this formula, you get for the monthly payment \r\n" );
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document.write( "    P = \"FV%2A%28r%2F%28%281%2Br%29%5En-1%29%29\".     (1)\r\n" );
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document.write( "Under the given conditions, FV = $10,000;  r = 0.08/12;  n = 8*12 = 96.  \r\n" );
document.write( "So, according to the formula (1), you get for the monthly payment \r\n" );
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document.write( "    P = \"10000%2A%28%28%280.08%2F12%29%29%2F%28%281%2B0.08%2F12%29%5E%288%2A12%29-1%29%29\" = $74.70.\r\n" );
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document.write( "Answer.  The necessary monthly deposit value is $74.70.\r\n" );
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document.write( "Note that of projected $10,000, the total of the deposits will be only  8*12 times $74.70, \r\n" );
document.write( "i.e. 8*12*74.70 = 7171.20 dollars. The rest is what the account will earn/accumulate in 8 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On Ordinary Annuity saving plans,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Ordinary Annuity saving plans\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.\r
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\n" ); document.write( "\n" ); document.write( "When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.\r
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\n" ); document.write( "\n" ); document.write( "To make such complicated calculations as they are in this problem,
\n" ); document.write( "you should have/use an appropriate calculator for such long formulas.\r
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\n" ); document.write( "\n" ); document.write( "Ideal choice is MS Excel, if you have it in your computer.\r
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\n" ); document.write( "\n" ); document.write( "Then you write a formula in a text editor, copy-paste it
\n" ); document.write( "into an Excel work-sheet cell and click \"enter\" - the result is ready
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\n" ); document.write( "\n" ); document.write( "If you have no MS Excel in your computer, you may find similar
\n" ); document.write( "free of charge calculators in the Internet. One such calculator is\r
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\n" ); document.write( "\n" ); document.write( "www.desmos.com/calculator\r
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\n" ); document.write( "\n" ); document.write( "It allows you to do the same thing: you write a formula in a text editor,
\n" ); document.write( "copy-paste it into this calculator and click \"enter\" - the result is ready
\n" ); document.write( "instantaneously.\r
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