Let's solve this step by step.

Information we know:

• Cost of the building: $7,200,000 (based on the appraisal).
• Original useful life: 30 years.
• Double-declining-balance method is being used for depreciation.
• Depreciation for Year 1: $480,000.
• Depreciation for Year 2: $448,000.
• In the third year, the estimated useful life was changed to 25 years (instead of 30).

Step 1: Calculate the book value at the beginning of Year 3.

• Book value after Year 1 = $7,200,000 − $480,000 = $6,720,000.
• Book value after Year 2 = $6,720,000 − $448,000 = $6,272,000.

Step 2: Determine the new depreciation rate for Year 3.

With the change in estimated useful life to 25 years, the remaining useful life at the beginning of Year 3 is now 23 years (25 years minus 2 years of prior depreciation).

• The double-declining-balance method uses a rate that is double the straight-line rate.
• New straight-line rate = $\frac{1}{25}$ = 4%.
• New double-declining rate = 4% × 2 = 8%.

Step 3: Calculate the depreciation expense for Year 3.

Now, apply the new double-declining rate (8%) to the book value at the beginning of Year 3:

$\text{Depreciation for Year 3} = 8\% \times 6,272,000 = 0.08 \times 6,272,000 = 501,760$

So, the depreciation expense for the third year is $501,760 (rounded to the nearest whole number).

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Would you like more details or have any questions?

Here are 5 related questions:

1. How is the straight-line method different from the double-declining-balance method?
2. How does changing the useful life affect depreciation calculations?
3. What would be the depreciation for Year 4 using the new useful life estimate?
4. What are some advantages of using the double-declining-balance method over other depreciation methods?
5. How do residual values impact depreciation in various methods?

Tip: When switching depreciation methods or changing estimates, always ensure that the accumulated depreciation doesn't exceed the asset's original cost.