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Math Help - SAT maths problem

  1. #1
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    Interest rate problem

    How much interest will $1000 earn in one year at an annual rate of 8%; if interest is compounded every 6 months?



    I've thought so far:

    At 8% in one year interest will be 80. But it is compounded every 6 months.

    So, after 6 months total amount will be $1040. Again at 8% in next 6 months, the amount will be $1081.6.


    Therefore, the interest will be $81.6. Is it right?
    Last edited by geton; October 20th 2010 at 11:04 AM.
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  2. #2
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    I believe you are right.
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  3. #3
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    Quote Originally Posted by geton View Post
    At 8% in one year interest will be 80. But it is compounded every 6 months.
    So, after 6 months total amount will be $1040. Again at 8% in next 6 months, the amount will be $1081.6
    Therefore, the interest will be $81.6. Is it right?
    Correct. Formula for Future Value of amount A:
    FV = A(1 + i)^n ; in your case, A=1000, i = .08/2 = .04, n = 2 (2 semiannual periods); so:
    FV = 1000(1.04)^2 = 1081.60

    If 6 years, then n=12 and:
    FV = 1000(1.04)^12 = 1601.03
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