The value of an antique chair is expected to increase by $3 \%$ every year. If the chair was bought for $\$ 1,020$ in 2001 , find its expected value in the year 2015 , rounded to the nearest dollar. \$

Step 1 ：The problem is asking for the future value of an investment with an annual interest rate of 3%. The formula for future value is: \(FV = PV * (1 + r)^n\) where: \(FV\) is the future value, \(PV\) is the present value, \(r\) is the interest rate, and \(n\) is the number of periods.

Step 2 ：In this case, the present value (\(PV\)) is the initial cost of the chair, $1,020. The interest rate (\(r\)) is 3%, or 0.03. The number of periods (\(n\)) is the number of years from 2001 to 2015, which is 14 years.

Step 3 ：Substituting the given values into the formula, we get: \(FV = 1020 * (1 + 0.03)^{14}\)

Step 4 ：Calculating the above expression, we get the future value (\(FV\)) to be approximately 1542.8415193522142

Step 5 ：Rounding this to the nearest dollar, we get \(FV = 1543\)

Step 6 ：Final Answer: The expected value of the chair in the year 2015 is \(\boxed{1543}\)