Reducing Rate Calculator
Calculate the diminishing value of a quantity over specific time intervals using a constant percentage reduction.
Calculation Results
Understanding Reducing Rate Calculations
A reducing rate calculation, often associated with geometric decay or diminishing returns, determines how an initial quantity decreases over time when a fixed percentage is removed at every interval. Unlike a linear reduction where a fixed amount is subtracted, a reducing rate applies to the current balance of the previous period.
The Reducing Rate Formula
The mathematical foundation for this calculator is the exponential decay formula:
Where:
- r is the reduction rate expressed as a decimal (e.g., 10% = 0.10).
- n is the number of time periods elapsed.
Practical Examples of Reducing Rates
This logic is applied across various fields outside of finance:
- Physics (Radioactive Decay): Calculating the remaining mass of an isotope after several half-life cycles.
- Chemistry (Concentration): Determining the dilution of a solution as a specific percentage is filtered out per cycle.
- Mechanical Engineering: Estimating the loss of pressure in a system or the wear of a component that degrades relative to its current state.
- Inventory Management: Calculating "shrinkage" or perishability where a portion of remaining stock is lost each day.
Why Constant Percentage Matters
The key characteristic of a reducing rate is that the absolute amount reduced becomes smaller in every period. For example, if you start with 1,000 and reduce by 10%, you lose 100 in the first period (leaving 900). In the second period, you lose 10% of 900, which is only 90. This creates a curve that approaches zero but never mathematically reaches it, representing a "diminishing" effect rather than a total depletion.