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, determine the value after 7 years.
The yearly depreciation of the machine is 15% of its value at the beginning of the year, or 0.15 * MK400,000.00 = MK60,000.00.
After the first year, the value of the machine will be MK400,000.00 - MK60,000.00 = MK340,000.00.
After the second year, the value will be MK340,000.00 - MK60,000.00 = MK280,000.00.
After the third year, the value will be MK280,000.00 - MK60,000.00 = MK220,000.00.
After the fourth year, the value will be MK220,000.00 - MK60,000.00 = MK160,000.00.
After the fifth year, the value will be MK160,000.00 - MK60,000.00 = MK100,000.00.
After the sixth year, the value will be MK100,000.00 - MK60,000.00 = MK40,000.00.
After the seventh year, the value will be MK40,000.00 - MK60,000.00 = -MK20,000.00.
Since the value cannot be negative, the value after 7 years is 0. Answer: \boxed{MK0.00}.
To determine the value of the machine after 7 years, we need to calculate the depreciation for each year and subtract it from the original cost.
Step 1: Calculate the depreciation for the first year
The depreciation for the first year is 15% of the original cost:
Depreciation = 15% of MK400,000.00
Depreciation = 0.15 x MK400,000.00
Depreciation = MK60,000.00
Step 2: Calculate the value after the first year
Value after 1 year = Original cost - Depreciation
Value after 1 year = MK400,000.00 - MK60,000.00
Value after 1 year = MK340,000.00
Step 3: Repeat steps 1 and 2 for each subsequent year, up to 7 years
Depreciation for each subsequent year = 15% of the value at the beginning of the year
Value after each subsequent year = Value after previous year - Depreciation for that year
After 2 years:
Depreciation = 15% of MK340,000.00
Depreciation = 0.15 x MK340,000.00
Depreciation = MK51,000.00
Value after 2 years = MK340,000.00 - MK51,000.00
Value after 2 years = MK289,000.00
After 3 years:
Depreciation = 15% of MK289,000.00
Depreciation = 0.15 x MK289,000.00
Depreciation = MK43,350.00
Value after 3 years = MK289,000.00 - MK43,350.00
Value after 3 years = MK245,650.00
Repeat this process for the remaining years up to 7 years.
After 4 years:
Depreciation = 15% of MK245,650.00
Depreciation = 0.15 x MK245,650.00
Depreciation = MK36,847.50
Value after 4 years = MK245,650.00 - MK36,847.50
Value after 4 years = MK208,802.50
After 5 years:
Depreciation = 15% of MK208,802.50
Depreciation = 0.15 x MK208,802.50
Depreciation = MK31,320.38
Value after 5 years = MK208,802.50 - MK31,320.38
Value after 5 years = MK177,482.12
After 6 years:
Depreciation = 15% of MK177,482.12
Depreciation = 0.15 x MK177,482.12
Depreciation = MK26,622.32
Value after 6 years = MK177,482.12 - MK26,622.32
Value after 6 years = MK150,859.80
After 7 years:
Depreciation = 15% of MK150,859.80
Depreciation = 0.15 x MK150,859.80
Depreciation = MK22,628.97
Value after 7 years = MK150,859.80 - MK22,628.97
Value after 7 years = MK128,230.83
Therefore, the value of the machine after 7 years is MK128,230.83.