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Math Help - Geometric Series Help (time payments)

  1. #1
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    Geometric Series Help (time payments)

    Hello, can someone help me with this.

    A man is to receive six payments of $500 each, the first payment in a year's time and subsequent payments at two-yearly intervals. He invests each payment at 9 per cent per annum. How much will he have immediately after the last payment is made. Answer is $4818

    and

    A firm is established with new equipment and creates a fund to provide for the replacement of the equipment after 6 years at an estimated cost of $20 000. How much should be paid into the fund anually if interest at 11 % can be obtained. Answer is $2528

    Can someone help me derive the equations...? I know how to do the rest. Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by noobonastick View Post
    Hello, can someone help me with this.

    A man is to receive six payments of $500 each, the first payment in a year's time and subsequent payments at two-yearly intervals. He invests each payment at 9 per cent per annum. How much will he have immediately after the last payment is made. Answer is $4818
    The last paymet is worth \$500, the one befor that \$500(1+9/100)^2 (that is the principle plus two years of interest compounded annually, the one before that \$500(1+9.100)^4, .. So the total is:

     <br />
500(1+1.09^2+1.09^4+1.09^6+1.09^8+1.09^{10})=500 \times\frac{1-(1.09^2)^{6}}{1-1.09^2}<br />
dollars

    CB
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  3. #3
    Member jonah's Avatar
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    Quote Originally Posted by noobonastick View Post
    A firm is established with new equipment and creates a fund to provide for the replacement of the equipment after 6 years at an estimated cost of $20 000. How much should be paid into the fund anually if interest at 11 % can be obtained. Answer is $2528
    Solve for R in the following
    <br />
20,000 = R\frac{{\left( {1.11} \right)^6  - 1}}<br />
{{.11}}<br />
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