1. ## 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) 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, $P = \120,000$
Amount with interest, $A= 2 \times \ 120,000 = \ 240, 000
$

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.