At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250 , find the value at the end of 5 years.
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Step-by-Step Solution
Step 1: Understand Depreciation
The problem states that the machine depreciates by 20% of its value at the beginning of each year. This means its value decreases by 20% annually. We are given the initial value, V0=Rs 1250, and the depreciation rate, r=20%=0.20.
Step 2: Calculate Value After One Year
After one year, the value of the machine will be its initial value minus the depreciation amount. This can be expressed as V0−V0×r, which simplifies to V0(1−r).
Step 3: General Formula for Depreciation
Since the depreciation occurs annually on the value at the beginning of that year, this is a case of compound depreciation. The value after n years, Vn, can be calculated using the formula Vn=V0(1−r)n.
Step 4: Substitute Values and Calculate
Now, we substitute the given values into the formula: V0=1250, r=0.20, and n=5. First, calculate (1−0.20)5=(0.80)5=0.32768. Then, multiply this by the initial value.
Step 5: Final Calculation
Performing the final multiplication, 1250×0.32768, we get the value of the machine at the end of 5 years.