Depreciation is the reduction in the value of an asset over time due to wear and tear, obsolescence or other factors. In this case, we are calculating the depreciation of a machine worth Rs.490,740.



The depreciation rate of the machine is given as 15% of its opening value each year. This means that every year, the value of the machine will decrease by 15% of its original value.



To calculate the depreciation of the machine each year, we can use the following formula:

Depreciation expense = Opening value of the asset x Depreciation rate

In the first year, the opening value of the machine is Rs.490,740. Therefore, the depreciation expense for the first year is:

Depreciation expense = Rs.490,740 x 15% = Rs.73,611

The value of the machine at the end of the first year can be calculated as:

Value of the machine at the end of the first year = Opening value of the asset - Depreciation expense

Value of the machine at the end of the first year = Rs.490,740 - Rs.73,611 = Rs.417,129

Similarly, the depreciation expense for the second year can be calculated as:

Depreciation expense = Rs.417,129 x 15% = Rs.62,570

The value of the machine at the end of the second year can be calculated as:

Value of the machine at the end of the second year = Rs.417,129 - Rs.62,570 = Rs.354,559

We can continue this calculation for each year until the value of the machine is reduced by 90%.



To calculate the number of years it will take for the value of the machine to be reduced by 90%, we can use the following formula:

Number of years = log(Ending value / Beginning value) / log(1 - Depreciation rate)

Where:
- Ending value = Beginning value - 90%
- Beginning value = Rs.490,740
- Depreciation rate = 15%

Using this formula, we get:

Number of years = log(0.1) / log(0.85)
Number of years = 5.63 years (rounded to two decimal places)

Therefore, it will take approximately 5.63 years for the value of the machine to be reduced by 90%.