To calculate the depreciation of a machine worth 490,740 over a period of time, we need to consider the rate of depreciation and the final value to which the machine's worth is reduced.



- Initial value of the machine: $490,740
- Rate of depreciation: 15%
- Final value of the machine: $200,000



To find out the number of years it takes for the machine's value to be reduced to $200,000, we can use the formula:

Final value = Initial value × (1 - Rate of depreciation)^n

Where "n" represents the number of years.

Substituting the given values:

$200,000 = $490,740 × (1 - 0.15)^n

Simplifying the equation:

0.15^n = 200,000 / 490,740

Taking the logarithm of both sides:

n × log(0.15) = log(200,000 / 490,740)

Solving for "n":

n = log(200,000 / 490,740) / log(0.15)

Using a calculator, we find that "n" is approximately 5.28 years.



It takes approximately 5.28 years for the machine's value to be reduced from $490,740 to $200,000, with a 15% depreciation rate annually.



- The machine is worth $490,740 initially.
- It is depreciated at a rate of 15% annually.
- The machine's value is reduced to $200,000 after approximately 5.28 years.