The yearly depreciation of a certain machine is 15% of its value at the beginning of the year. If the original cost of the machine is MK400,000.00, using either skills of either arithmetic progression or geometric progression,determine the value after 7 years.

Answer 1

If the machine depreciates by 15% every year, its value at the end of each year can be calculated using geometric progression.

Let V be the value of the machine at the beginning of the year.
After the first year, the value of the machine will be V - 0.15V = 0.85V.
After the second year, the value of the machine will be 0.85V - 0.15(0.85V) = 0.85V - 0.1275V = 0.7225V.
Similarly, we can calculate the value of the machine at the end of each subsequent year.

The value of the machine at the end of 7 years can be calculated as follows:
V7 = 0.85V6 = 0.85(0.85V5) = 0.85(0.85(0.85V4)) = ... = 0.85^7 * V

Using the given information, we can calculate the value of the machine after 7 years:
V7 = 0.85^7 * 400,000
≈ 0.2217 * 400,000
≈ 88,681.70

Therefore, the value of the machine after 7 years is approximately MK88,681.70.