# APY Calculation

## The Formula

APY (Annual Percentage Yield) with compound interest:

```
APY = (1 + r)^n - 1
```

Where:

* **r** = interest rate per period
* **n** = number of periods per year

***

## Crypto DAO Specifics

| Parameter         | Value                       |
| ----------------- | --------------------------- |
| Rebase frequency  | Every 12 hours (2× per day) |
| Rebase rate range | 0.5% – 0.9% per rebase      |
| Rate adjustment   | Based on network debt ratio |

***

## Calculation Examples

{% tabs %}
{% tab title="Minimum Rate (0.5%)" %}
**Per-rebase rate:** 0.5%

```
APY = (1 + 0.005)^730 - 1
APY = (1.005)^730 - 1
APY ≈ 38.08 - 1
APY ≈ 3,708%
```

{% endtab %}

{% tab title="Mid Rate (0.7%)" %}
**Per-rebase rate:** 0.7%

```
APY = (1 + 0.007)^730 - 1
APY = (1.007)^730 - 1
APY ≈ 163.56 - 1
APY ≈ 16,256%
```

{% endtab %}

{% tab title="Maximum Rate (0.9%)" %}
**Per-rebase rate:** 0.9%

```
APY = (1 + 0.009)^730 - 1
APY = (1.009)^730 - 1
APY ≈ 694.44 - 1
APY ≈ 69,344%
```

{% endtab %}
{% endtabs %}

***

## With Period Bonuses

Longer lock-ups receive bonus rates on top of base rebase:

| Lock Period | Bonus | Effective Rebase | Approx. APY |
| ----------- | ----- | ---------------- | ----------- |
| 1 day       | +0%   | 0.50%            | \~3,708%    |
| 30 days     | +5%   | 0.525%           | \~4,454%    |
| 90 days     | +10%  | 0.55%            | \~5,340%    |
| 180 days    | +15%  | 0.575%           | \~6,388%    |
| 360 days    | +30%  | 0.65%            | \~10,512%   |
| 540 days    | +45%  | 0.725%           | \~18,957%   |

{% hint style="info" %}
These estimates assume 0.5% base rate. Actual APY varies as base rate adjusts with network conditions.
{% endhint %}

***

## Simple Projection Table

Starting with **1,000 PRO** at different base rebase rates:

| Time     | 0.5% Rebase | 0.7% Rebase | 0.9% Rebase |
| -------- | ----------- | ----------- | ----------- |
| 30 days  | 1,349 PRO   | 1,520 PRO   | 1,713 PRO   |
| 90 days  | 2,456 PRO   | 3,513 PRO   | 5,026 PRO   |
| 180 days | 6,032 PRO   | 12,343 PRO  | 25,260 PRO  |
| 365 days | 37,078 PRO  | 162,560 PRO | 693,440 PRO |

The power of compound interest grows dramatically over time.

***

## Why APY Varies

{% tabs %}
{% tab title="Factors" %}
**What affects the base rate:**

* Network debt ratio
* Total staked PRO
* Treasury reserves
* Protocol runway

Higher debt = lower rebase rate to maintain sustainability.
{% endtab %}

{% tab title="APY ≠ Profit" %}
**Important distinction:**

APY measures token quantity growth, not USD value.

* Your PRO balance increases
* PRO price may fluctuate
* Net profit = balance × price change

High APY with falling price can still mean loss.
{% endtab %}

{% tab title="Not Guaranteed" %}
**APY is not fixed:**

* Base rate adjusts algorithmically
* Network conditions change
* Past rates don't guarantee future rates

Check the dApp dashboard for current live rate.
{% endtab %}
{% endtabs %}

***

## Calculator

Your projection formula:

```
Starting PRO × (1 + rebase_rate)^(days × 2) = Ending PRO
```

Example at 0.5% rebase:

```
1,000 × (1.005)^730 = 37,078 PRO
```

***

## Related

* [How Staking Works](broken://pages/6b7fa4bf9879131aac20fb69fef128c8ca78fa03)
* [Lock Periods](broken://pages/0609abb943a12af4286285d039c1d0f76d476ee4)
* [Dynamic Balance](broken://pages/e7b2ed6121af8f8497c0949d8a397c5dc60bc5de)


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