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Thread: 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, $\displaystyle P = \$120,000$
    Amount with interest, $\displaystyle A= 2 \times \$ 120,000 = \$ 240, 000
    $
    Let rate of interest $\displaystyle = i $

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

    $\displaystyle A = P (1 + i)^n$

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

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

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

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

    $\displaystyle 1+i=1.0293$

    $\displaystyle i=0.0293$

    $\displaystyle i=0.0293 \times 2 \times 100 \%$

    $\displaystyle i=5.86 \% $ semiannually.
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