Question

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Explanation:

Step1: Recall Compound Growth Formula

The formula for compound growth (or appreciation) is \( V(t) = P(1 + r)^t \), where \( P \) is the principal amount, \( r \) is the annual growth rate (as a decimal), and \( t \) is time in years.

Step2: Identify Values

Here, \( P = 1000 \) (the initial investment), and the annual appreciation rate is \( 4\% = 0.04 \). So \( r = 0.04 \).

Step3: Substitute into Formula

Substituting \( P = 1000 \) and \( r = 0.04 \) into the formula gives \( V(t) = 1000(1 + 0.04)^t \), which matches option D. The other options use incorrect rates (e.g., 0.4 or 0.04 without adding 1, which is not the growth formula).

Answer:

D. \( V(t) = 1000(1 + 0.04)^t \)