document.write( "Question 1111913: Rachel Spender wants to invest $4000 in savings certificates which bear an interest rate of 7.25% compounded semi-anually. How long a time period should she choose in order to save an amount of $4700? \n" ); document.write( "

Algebra.Com's Answer #853999 by MathTherapy(10801) $\"\"$ $\"About$

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document.write( "Rachel Spender wants to invest $4000 in savings certificates which bear an interest rate of 7.25% compounded semi-anually. How long a time period should she choose in order to save an amount of $4700?\r\n" );
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document.write( "Future-value-of-$1 formula: , with  = Future Value (Unknown, in this case)\r\n" );
document.write( "                                                                                         = Principal/Initial Deposit ($4,000, in this case)\r\n" );
document.write( "                                                                                         = Interest rate, as a decimal (7.25%, or .0725, in this case)\r\n" );
document.write( "                                                                                         = Number of ANNUAL compounding periods (semiannually, or 2, in this case)\r\n" );
document.write( "                                                                                         = Time Principal/Initial Deposit has been invested, in YEARS (t, in this case)\r\n" );
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document.write( "How long a time period should she choose in order to save an amount of $4700?\r\n" );
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document.write( "                                                                ----- Substituting $4,700 for A, $4,000 for P, .0725 for i, and 2 for m \r\n" );
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document.write( "                                                                      ----- Converting to LOGARITHMIC form\r\n" );
document.write( "Time it'll take the $4,000 investment to increase to $4,700, or  = 2.26446601 years, which needs to be ROUNDED UP\r\n" );
document.write( "                                                                                                                                                             to  years, or 2 years, 6 months.\r\n" );
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document.write( "** Notice that although 2.26446601 rounds off to about  years, the $4,000 investment, at the -year juncture, will increase to about\r\n" );
document.write( "$4,695.16 (< $4,700). This is why it's necessary to ROUND UP to year , or 2.5 years (at the semi-annual point), at which time, the $4,000 \r\n" );
document.write( "initial deposit will exceed $4,700 (about $4,779.50, to be exact).

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