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Sagot :
To determine how much a car worth K135,000.00 this year will depreciate to over three years given an annual depreciation rate of 15%, we need to follow a step-by-step process of calculating the car's value at the end of each year.
### Step-by-Step Solution:
1. Initial Value:
The initial value of the car is K135,000.00.
2. First Year Depreciation:
The car depreciates by 15% in the first year.
[tex]\[ \text{Depreciation Amount (Year 1)} = \text{Initial Value} \times \text{Depreciation Rate} \][/tex]
[tex]\[ \text{Depreciation Amount (Year 1)} = 135,000.00 \times 0.15 = 20,250.00 \][/tex]
[tex]\[ \text{Value After 1 Year} = \text{Initial Value} - \text{Depreciation Amount (Year 1)} \][/tex]
[tex]\[ \text{Value After 1 Year} = 135,000.00 - 20,250.00 = 114,750.00 \][/tex]
3. Second Year Depreciation:
The car now depreciates another 15% on its new value after the first year.
[tex]\[ \text{Depreciation Amount (Year 2)} = \text{Value After 1 Year} \times \text{Depreciation Rate} \][/tex]
[tex]\[ \text{Depreciation Amount (Year 2)} = 114,750.00 \times 0.15 = 17,212.50 \][/tex]
[tex]\[ \text{Value After 2 Years} = \text{Value After 1 Year} - \text{Depreciation Amount (Year 2)} \][/tex]
[tex]\[ \text{Value After 2 Years} = 114,750.00 - 17,212.50 = 97,537.50 \][/tex]
4. Third Year Depreciation:
The car now depreciates another 15% on its new value after the second year.
[tex]\[ \text{Depreciation Amount (Year 3)} = \text{Value After 2 Years} \times \text{Depreciation Rate} \][/tex]
[tex]\[ \text{Depreciation Amount (Year 3)} = 97,537.50 \times 0.15 = 14,630.625 \][/tex]
[tex]\[ \text{Value After 3 Years} = \text{Value After 2 Years} - \text{Depreciation Amount (Year 3)} \][/tex]
[tex]\[ \text{Value After 3 Years} = 97,537.50 - 14,630.625 = 82,906.875 \][/tex]
### Conclusion:
After three years, the car will be worth approximately K82,906.88.
### Step-by-Step Solution:
1. Initial Value:
The initial value of the car is K135,000.00.
2. First Year Depreciation:
The car depreciates by 15% in the first year.
[tex]\[ \text{Depreciation Amount (Year 1)} = \text{Initial Value} \times \text{Depreciation Rate} \][/tex]
[tex]\[ \text{Depreciation Amount (Year 1)} = 135,000.00 \times 0.15 = 20,250.00 \][/tex]
[tex]\[ \text{Value After 1 Year} = \text{Initial Value} - \text{Depreciation Amount (Year 1)} \][/tex]
[tex]\[ \text{Value After 1 Year} = 135,000.00 - 20,250.00 = 114,750.00 \][/tex]
3. Second Year Depreciation:
The car now depreciates another 15% on its new value after the first year.
[tex]\[ \text{Depreciation Amount (Year 2)} = \text{Value After 1 Year} \times \text{Depreciation Rate} \][/tex]
[tex]\[ \text{Depreciation Amount (Year 2)} = 114,750.00 \times 0.15 = 17,212.50 \][/tex]
[tex]\[ \text{Value After 2 Years} = \text{Value After 1 Year} - \text{Depreciation Amount (Year 2)} \][/tex]
[tex]\[ \text{Value After 2 Years} = 114,750.00 - 17,212.50 = 97,537.50 \][/tex]
4. Third Year Depreciation:
The car now depreciates another 15% on its new value after the second year.
[tex]\[ \text{Depreciation Amount (Year 3)} = \text{Value After 2 Years} \times \text{Depreciation Rate} \][/tex]
[tex]\[ \text{Depreciation Amount (Year 3)} = 97,537.50 \times 0.15 = 14,630.625 \][/tex]
[tex]\[ \text{Value After 3 Years} = \text{Value After 2 Years} - \text{Depreciation Amount (Year 3)} \][/tex]
[tex]\[ \text{Value After 3 Years} = 97,537.50 - 14,630.625 = 82,906.875 \][/tex]
### Conclusion:
After three years, the car will be worth approximately K82,906.88.
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