document.write( "Question 213128: $1,500 is deposited every year in an account yielding 6% interest compounded annually. How much money will have been saved after 10 years? \n" ); document.write( "

Algebra.Com's Answer #161017 by Edwin McCravy(20060) $\"\"$ $\"About$

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$1,500 is deposited every year in an account yielding 6% interest compounded annually. How much money will have been saved after 10 years?
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document.write( "The formula for the amount,$A an initial investment of \r\n" );
document.write( "$P will grow to in t years is given by:\r\n" );
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document.write( "A = P(1+r)^t\r\n" );
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document.write( "The $1500 deposited at the beginning of the 10th year \r\n" );
document.write( "will have grown to $1500(1+r)^1 in the 1 year it will \r\n" );
document.write( "have been on deposit at the end of the 10th year.\r\n" );
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document.write( "The $1500 deposited at the beginning of the 9th year \r\n" );
document.write( "will have grown to $1500(1+r)^2 in the 2 years it will \r\n" );
document.write( "have been on deposit at the end of the 10th year.\r\n" );
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document.write( "The $1500 deposited at the beginning of the 8th year \r\n" );
document.write( "will have grown to $1500(1+r)^3 in the 3 years it will \r\n" );
document.write( "have been on deposit at the end of the 10th year.\r\n" );
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document.write( "...\r\n" );
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document.write( "The $1500 deposited at the beginning of the 2nd year \r\n" );
document.write( "will have grown to $1500(1+r)^9 in the 9 years it will \r\n" );
document.write( "have been on deposit at the end of the 10th year.\r\n" );
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document.write( "The $1500 deposited at the beginning of the 1st year \r\n" );
document.write( "will have grown to $1500(1+r)^10 in the 10 year it will \r\n" );
document.write( "have been on deposit at the end of the 10th year.\r\n" );
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document.write( "So the sum is this series:\r\n" );
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document.write( "$1500(1+r) + $1500(1+r)^2 + $1500(1+r)^3 + ... + $1500(1+r)^10\r\n" );
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document.write( "and since r = 6% = .06\r\n" );
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document.write( "$1500(1.06) + $1500(1.06)^2 + $1500(1.06)^3 + ... + $1500(1.06)^10\r\n" );
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document.write( "The common ratio is 1.06, so we use the formula for the sum\r\n" );
document.write( "of the first n terms of a geometric series:\r\n" );
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document.write( "Substituting ,  and \r\n" );
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document.write( "Edwin

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