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) 2. Originally Posted by euclid2 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.