Final answer:
The one-year appreciation rate is 4.4%, which is calculated by determining the rate of increase in value over two years and then dividing by two.
Step-by-step explanation:
To determine the one-year appreciation rate, we must calculate the percentage increase in the value of the home from the initial cost to its value two years later and then divide by the number of years. The initial cost was $540,000, and it appreciated to $588,000 in two years. The increase in value is $588,000 - $540,000 = $48,000. Over the span of two years, this equates to an appreciation rate of ($48,000 ÷ $540,000) × 100% per year. Dividing this by 2 gives the one-year appreciation rate.
The appreciation rate is ($48,000 ÷ $540,000) × 100% = 8.888...%, which when divided by 2 results in approximately 4.44%. Therefore, the correct answer to the student's question is (b) 4.4%.