Final answer:
To find out how many years an asset has been depreciated under the declining balance method with a 25% depreciation rate, we apply the rate to the asset's original cost until we match the current book value. The closest match to the given current book value after applying the formula is 5 years.
Step-by-step explanation:
To calculate how many years an asset has been in service using the declining balance depreciation method with a 25% depreciation rate, you need to apply the depreciation rate to the book value at the end of each year until you reach the current book value of the asset. The formula for the declining balance method is:
Book Value at end of year n = Cost of Asset × (1 - Depreciation Rate)n
Given the following:
- Original cost of the asset = $30,000
- Current book value = $7,119.14
- Depreciation rate = 25%
Plugging the numbers into the formula and solving for n (the number of years), you can calculate the number of years the asset has been in service. After doing the calculations, we find that the closest number of years that gets us to the current book value of $7,119.14 is 5 years. Hence, the answer is (b) 5 years.