An investment decreases by 4% per year for 3 years. By what total percent does it decrease after the 3 years?
An investment decreases by 4% per year for 3 years. By what total percent does it decrease after the 3 years?
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To find the total percent decrease after 3 years, we need to calculate the cumulative effect of the 4% decrease for each year.
First, let's calculate the decrease for each year:
Year 1: The investment decreases by 4%.
Year 2: The investment decreases by 4% of the previous year's value, which is now 96% of the original value.
Year 3: The investment decreases by 4% of the previous year's value, which is now 96% * 96% of the original value.
To find the total percent decrease, we need to calculate the final value as a percentage of the original value:
Final Value = Original Value * (0.96 * 0.96 * 0.96)
To find the percent decrease, we need to subtract the final value from the original value, divide by the original value, and multiply by 100:
Percent Decrease = ((Original Value - Final Value) / Original Value) * 100
Now we can calculate the total percent decrease after 3 years. Let's assume the original value is 100:
Final Value = 100 * (0.96 * 0.96 * 0.96) ≈ 87.4752
Percent Decrease = ((100 - 87.4752) / 100) * 100 ≈ 12.525%
Therefore, the investment decreases by approximately 12.525% after 3 years.