The value of the stamp increases by 5% each year. This can be modeled by the formula for compound interest:

\(V = P(1 + r)^n\)

where \(V\) is the future value, \(P\) is the initial principal ($10,000), \(r\) is the annual increase rate (0.05), and \(n\) is the number of years (2015 - 2005 = 10 years).

Substitute the values into the formula:

\(V = 10000 \times (1.05)^{10}\)

Calculate \((1.05)^{10}\):

\((1.05)^{10} \approx 1.62889\)

Then, calculate the future value:

\(V = 10000 \times 1.62889 \approx 16288.9\)

Round to the nearest $100:

\(V \approx 16300\)

Therefore, the value of the stamp at the beginning of 2015 is $16,300.