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Math Help - financial mathematics

  1. #1
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    financial mathematics

    a family wishes to accumulate $50000 in a college education fund att rhe end of 20 years. If they deposit $1000 in the fund at the end of each of the first 10 years and $1000+X in the fund at the end of each of the second 10 years, find X to the nearest dollar if fund earns an effective interest annual rate of 7%
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  2. #2
    MHF Contributor
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    Do it in 3 steps:

    1: $1000 deposited for 10 years at 7% annually = 13,816.45

    2: $13,816.45 @ 7% annually for 10 years (11 to 20) = 27,179.04

    So the amount that the new annual deposit of 1000+x must accumulate
    to over 10 years (11 to 20) is 50,000 - 27,179.04 = 22,820.96

    3: Annual deposit for 10 years (11 to 20) at 7% annually that
    accumulates to 22,820.96 = 1,651.72 ; so x = 651.72

    This can be easily done by using financial formulas; as example:
    (1000 + x)(1.07^10 - 1) / .07 = 22820.96
    Solve for x: 651.72

    Now YOU do some work: find the formulas
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