Scrap Value = 30,000
cost of machine = 1,00,000
Rate = 20%
scrap Value = cost × ( 1-Rate of reducing )n
30,000 = 1,00,000 × ( 1-20%) n
0.3 = (0.8) n
(0.8)⁵ = (0.8) n
n = 5

Effective Life of the Machine

To find the effective life of the machine, we need to understand the concept of depreciation and the formula used for calculating depreciation in this case.

Depreciation:
Depreciation is the decrease in the value of an asset over time due to wear and tear, obsolescence, or other factors. It is a way to allocate the cost of an asset over its useful life.

Reducing Balance Method:
The reducing balance method is a common method used to calculate depreciation. In this method, the depreciation expense is calculated as a fixed percentage of the asset's book value at the beginning of each accounting period. The book value is the original cost of the asset minus the accumulated depreciation.

Given Information:
- Original cost of machinery: $100,000
- Ultimate salvage value of machinery: $30,000
- Depreciation rate: 20% on reducing balance

Calculation:
1. Determine the annual depreciation expense using the reducing balance method:
- Depreciation expense = Book value at the beginning of the year * Depreciation rate
- Book value at the beginning of the year = Original cost - Accumulated depreciation

2. Calculate the accumulated depreciation over the years:
- Accumulated depreciation = Depreciation expense for the first year + Depreciation expense for the second year + ...

3. Determine the effective life of the machine:
- Effective life = Original cost - Ultimate salvage value / Accumulated depreciation

Example Calculation:
Let's calculate the effective life of the machine using the given information.

1. Annual depreciation expense for the first year:
- Book value at the beginning of the year = $100,000 - $0 (no accumulated depreciation yet)
- Depreciation expense = $100,000 * 20% = $20,000

2. Accumulated depreciation after the first year:
- Accumulated depreciation = $20,000

3. Effective life of the machine:
- Effective life = ($100,000 - $30,000) / $20,000 = 3.5 years

Therefore, the effective life of the machine is 3.5 years.

Summary:
The effective life of the machine can be calculated by determining the annual depreciation expense using the reducing balance method, calculating the accumulated depreciation over the years, and then dividing the difference between the original cost and the ultimate salvage value by the accumulated depreciation. In this case, the effective life of the machine is calculated to be 3.5 years.