# 🏦The Bank

Users can burn PDO to receive PBD at any time during the **contraction **state.

User can redeem PBD to receive PDO back with profits when the protocol returns to the Expansion state.

Each **Contraction Epoch** will last for 6 hours.

To encourage users to hold PBD Bond even when PDO's TWAP > 1, Bond redemption will provide more profits when PDO has a higher value. The conversion rate from PBD to PDO will be 1:R, with R calculated according to the formula:

R = 1 + min[0.3, (PDO_TWAP_Price - 1)*coeff ]

coeff = 0.75

When the user redeems PBD for PDO, these PDO will be paid from the Protocol's Treasury reserve.

### Example:

The PDO price dropped to 0.9 USDC, and Alice and Bob both purchased 100 PBD Bonds. Then, the PDO price increased again to 1.1 USDC. Alice redeemed PBD at a PDO price of 1.1 USDC, while Bob redeemed PBD at a PDO price of 1 USDC.

In this scenario,

Alice spent 90 USDC to buy 100 PDO. She burned these 100 PDO to receive 100 PBD.

When the PDO price increased to 1.1 USDC, Alice exchanged 100 PBD with R:

R = 1 + min[0.3, (1.1-1)*0.75] = 1 + min[0.3, 0.075] = 1.075.

Alice received 107.5 PDO. If Alice continues to swap PDO for USDC, she will receive 118.25 USDC. This generates a profit of 31.38% when the PDO price increases from 0.9 USDC to 1.1 USDC (a 22.22% increase).

Bob spent 90 USDC to buy 100 PDO. He burned these 100 PDO to receive 100 PBD.

When the PDO price increased to 1 USDC, Bob exchanged 100 PBD with R:

R = 1 + min[0.3, (1-1)*0.75] = 1 + min[0.3, 0] = 1.

Bob received 100 PDO. If Bob continues to swap PDO for USDC, he will receive 100 USDC. This generates a profit of 11.11%, equivalent to the increase in PDO price from 0.9 to 1 USDC.

Exchanging PDO for PBD in the Expansion state will result in net loss.

To avoid this, the protocol's interface will disable the function of exchanging PDO for PBD in the Expansion state.

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