document.write( "Question 1133083: Terry mother figures that she will need to have $200 000 at the end of 10 years. The retirement fund that she has chosen earns interest at 6% compounded semi-annually.\r
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Algebra.Com's Answer #750260 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "Terry's mother figures that she will need to have $200 000 at the end of 10 years.
\n" ); document.write( "The retirement fund that she has chosen earns $\"highlight%28annual%29\"$ interest at 6% compounded semi-annually.\r
\n" ); document.write( "\n" ); document.write( "A) How much does she need to invest in the fund every six months?\r
\n" ); document.write( "\n" ); document.write( "B) how much interest will Terry's mother have earned over the course of her investment?
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document.write( "It is a classic Ordinary Annuity saving plan. 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 payment (deposit); r is the semi-annual percentage yield 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 payment \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 = 0.06/2;  n = 10*2 = 20.  So, according to the formula (1), you get for the semi-annual payment \r\n" );
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document.write( "    P =  = $7443.14.\r\n" );
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document.write( "Answer to question (A) :    The necessary semi-annual deposit value is $7443.14.\r\n" );
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document.write( "Note that of projected $200,000 the total of mother's deposits will be only  10*2 times $7443.14, i.e. 10*2*7443.14 = 148862.80 dollars.\r\n" );
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document.write( "Answer to question (B) :  The interest mother will have earned over the course of her investment is   = 34.35%.    \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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