Calculating your final value is straightforward once you know the Exponential Decay formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Exponential Decay Calculator.
What is Exponential Decay?
The Exponential Decay calculation tells you your final value from a few simple inputs. The figure you are solving for here is the final value.
The Exponential Decay formula
The core formula is:
Final value = Initial value × (1 - Decay rate per period ÷ 100)^(Number of periods)Here is what each input means:
- Initial value — a number. Example: 1,000.
- Decay rate per period — a percentage, such as an annual rate. Example: 5%.
- Number of periods — a number. Example: 10.
How to calculate it step by step
- Write down the initial value (for example, 1,000).
- Write down the decay rate per period (for example, 5%).
- Write down the number of periods (for example, 10).
- Apply the formula above to get your final value.
- Double-check the result with the Exponential Decay Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Initial value | 1,000 |
| Decay rate per period | 5% |
| Number of periods | 10 |
| Final value | 598.74 |
| Total decrease | 401.26 |
With initial value of 1,000, decay rate per period of 5% and number of periods of 10, the final value works out to 598.74.
Example 2
With initial value of 2,000, decay rate per period of 5% and number of periods of 10, the final value works out to 1,197.47.
| Result | Value |
|---|---|
| Final value | 1,197.47 |
| Total decrease | 802.53 |
Example 3
With initial value of 500, decay rate per period of 5% and number of periods of 10, the final value works out to 299.37.
| Result | Value |
|---|---|
| Final value | 299.37 |
| Total decrease | 200.63 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Exponential Decay Calculator does it instantly, for free, with the formula and a worked example built in.
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