document.write( "Question 1185409: You wish to purchased a house for $200,000 in 12 years. You can invest your money at 5%/a compounded semiannually. How much do you need to invest every 6 months, starting in 6 months, so that you will have $200,000 at the time of your last deposit? (Hint: You need to find the value for \"a\". )
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Algebra.Com's Answer #849632 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "You wish to purchased a house for $200,000 in 12 years.
\n" ); document.write( "You can invest your money at 5% compounded semiannually.
\n" ); document.write( "How much do you need to invest every 6 months, starting in 6 months,
\n" ); document.write( "so that you will have $200,000 at the time of your last deposit?
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document.write( "This problem is about ordinary annuity.\r\n" );
document.write( "They want you to determine regular semi-annual deposits to get\r\n" );
document.write( "$200,000 in 12 years, depositing at 5% compounded semiannually.\r\n" );
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document.write( "The general formula is \r\n" );
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document.write( "    FV = ,    \r\n" );
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document.write( "where  FV is the future value of the account;  P is the semi-annual deposit value; \r\n" );
document.write( "r is the semi-annual effective rate presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of years multiplied by 2, in this case).\r\n" );
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document.write( "From this formula, you get for the semi-annual deposit value \r\n" );
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document.write( "    P = .     (1)\r\n" );
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document.write( "Under the given conditions, FV = $200,000;  r = 0.05/2 = 0.025;  n = 12*2 = 24.  \r\n" );
document.write( "So, according to the formula (1), you get for the semi-annual deposit value\r\n" );
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document.write( "    P =  = 6182.57  (rounded to closest greater cent).\r\n" );
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document.write( "Answer.  The necessary semi-annual deposit value is $6182.57.\r\n" );
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