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    chuk1279 Posts: 1, Reputation: 1
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    #1

    Jul 22, 2012, 01:50 PM
    Find the annual interest rate.
    Present Value Future Value Time Period Annual Interest Rate
    $ 100 $ 118.76 3 years %
    200 271.09 4 %
    100 115.37 5 %
    fivestarstar's Avatar
    fivestarstar Posts: 7, Reputation: 1
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    #2

    Jul 23, 2012, 01:56 AM
    Quote Originally Posted by chuk1279 View Post
    Present Value Future Value Time Period Annual Interest Rate
    $ 100 $ 118.76 3 years %
    200 271.09 4 %
    100 115.37 5 %
    All answers are to three significant figures.

    For simple interest, I = PRT / 100, i.e. R = 100I / PT

    Therefore, the answer to the first question is 100 x (118.76-100) / (100 x 3) = 6.25, i.e. 6.25% p.a..

    The answer to the second question is 100 x (271.09-200) / (200 x 4) = 8.89, i.e. 8.89% p.a.

    The answer to the third question is 100 x (115.37-100) / (100x 5) = 3.07, i.e. 3.07% p.a.

    For compound interest, A = P(1 + R/100)^n

    First question:
    118.76 = 100 (1 + R/100)^3
    1.1876 = (1 + R/100)^3
    cube root of 1.1876 = 1 + R/100
    cube root of 1.1876 - 1 = R/100
    100 (cube root of 1.1876 - 1) = R
    5.90 = R
    R = 5.90

    Therefore, the interest rate is 5.90%.

    Second question:
    271.09 = 200 (1 + R/100)^4
    1.35545 = (1 + R/100)^4
    fourth root of 1.35545 = 1 + R/100
    fourth root of 1.35545 - 1 = R/100
    100 (fourth root of 1.35545 - 1) = R
    7.90 or -208 (rejected) = R
    R = 7.90

    Therefore, the interest rate is 7.90%.


    Third question:
    115.37 = 100 (1 + R/100)^5
    1.1537 = (1 + R/100)^5
    fifth root of 1.1537 = 1 + R/100
    fifth root of 1.1537 - 1 = R/100
    100 (fifth root of 1.1537 - 1) = R
    2.90 = R
    R = 2.90


    Therefore, the interest rate is 2.90%.

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