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.
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.
To determine the value of the machine after 7 years, we can use the concept of geometric progression.
In geometric progression, each term is obtained by multiplying the previous term by a common ratio. In this case, the common ratio is (100% - 15%) = 85%, or 0.85 in decimal form.
We can calculate the value of the machine after each year using the formula:
Value after year n = Original cost * (Common ratio)^n
Given:
Original cost = MK400,000.00
Common ratio = 0.85
Number of years = 7
Let's calculate the value of the machine after 7 years:
Value after 1 year = MK400,000.00 * (0.85)^1
Value after 1 year = MK400,000.00 * 0.85
Value after 1 year = MK340,000.00
Value after 2 years = MK400,000.00 * (0.85)^2
Value after 2 years = MK400,000.00 * 0.7225
Value after 2 years = MK289,000.00
Value after 3 years = MK400,000.00 * (0.85)^3
Value after 3 years = MK400,000.00 * 0.614125
Value after 3 years = MK245,650.00
Value after 4 years = MK400,000.00 * (0.85)^4
Value after 4 years = MK400,000.00 * 0.52150625
Value after 4 years = MK208,602.50
Value after 5 years = MK400,000.00 * (0.85)^5
Value after 5 years = MK400,000.00 * 0.44328031
Value after 5 years = MK177,312.12
Value after 6 years = MK400,000.00 * (0.85)^6
Value after 6 years = MK400,000.00 * 0.37678826
Value after 6 years = MK150,715.30
Value after 7 years = MK400,000.00 * (0.85)^7
Value after 7 years = MK400,000.00 * 0.32027001
Value after 7 years = MK128,108.00
Therefore, the value of the machine after 7 years is MK128,108.00.