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Math Help - compound interest

  1. #1
    Senior Member euclid2's Avatar
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    compound interest

    Your parents purchased a house for $120,000. After 12 years the house had doubled in value. What was the interest rate that could generate this return on their investment if the rate were compounded semiannually? (Hint: the 24th root is equal to an exponent of 1/24)
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  2. #2
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    Quote Originally Posted by euclid2 View Post
    Your parents purchased a house for $120,000. After 12 years the house had doubled in value. What was the interest rate that could generate this return on their investment if the rate were compounded semiannually? (Hint: the 24th root is equal to an exponent of 1/24)
    Principal amount, P = \$120,000
    Amount with interest, A= 2 \times \$ 120,000 = \$ 240, 000<br />
    Let rate of interest = i

    Number of interest periods = n = 2 \times 12 = 24

    A = P (1 + i)^n

    240,000 = 120,000 (1+i)^{24}

    2 = (1+i)^{24}

    (1+i)=\sqrt[24]{2}

    (1+i)=2^{\frac{1}{24}}

    1+i=1.0293

    i=0.0293

     i=0.0293 \times 2 \times 100 \%

     i=5.86 \% semiannually.
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