Saving

📘 What is Saving?

The Saving service allows users to earn time-based interest on their deposited assets. These assets are efficiently managed within the protocol to provide sustainable and stable returns.

• Key Features:

  • Stable Yield: Powered by a time-based ESD Savings Rate (ESR).

  • Compound Growth: Accumulated interest is added to the principal continuously.

  • User-Friendly Interface: Simple deposit and withdrawal functionality.

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📊 Key Concepts

1. ESR (Esd Savings Rate)

• Definition: The continuous annual interest rate applied per second.

• Management:

  • Governed by the protocol's governance mechanism.

  • Provides stable returns by accumulating interest over time.

• Unit: ray (fixed-point, (10^{27})).

DSR Calculation Formula

• ( r ): Per-second interest rate.

• ( Δt ): Time elapsed since the last update.

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2. CHI (Rate Accumulator)

• Definition: Tracks the cumulative interest rate over time.

• Role:

  • Used to calculate the total value of deposited assets, including interest.

  • Updated whenever the drip function is called.

CHI Calculation Flow

1. ( chi_next = chi_current \times r^{Δt} )

2. ( total_value = pie \times chi )

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🛠️ How to Use

1. Deposit (Join)

Users can start earning savings by depositing their assets into the protocol.

• Steps:

  1. Call the join function on the smart contract.

  2. The deposited amount is stored in pie, and interest is accumulated based on chi.

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2. Withdraw (Exit)

Users can withdraw their deposits at any time.

• Steps:

  1. Call the exit function.

  2. The total amount (principal + interest) is calculated using chi and transferred to the user.

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💡 Key Benefits

1. Stable Returns:

   • Sustainable interest rate powered by protocol revenue.

2. Flexible Withdrawals:

   • Users can withdraw their savings anytime.

3. Governance-Controlled Rate:

   • ESR can be adjusted by governance to maintain protocol liquidity and stability.

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🧑‍💻 Smart Contract Specification

Key Functions

1. join(uint256 wad):

   • Deposits assets into the protocol.

   • wad: The amount to deposit.

   • The normalized deposit is stored in pie[msg.sender].

2. exit(uint256 wad):

   • Withdraws assets from the protocol.

   • wad: The amount to withdraw.

3. drip():

   • Updates the interest rate (chi) and last update timestamp (rho).

4. file(bytes32 what, uint256 data):

   • Sets the ESR value.

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📈 Example: Earning with Saving

Initial Conditions:

• DSR: 1000000002293273137447730714 (approximately 7.5% annual interest rate).

• Deposit Amount: 1,000 ESD.

Over Time:

1. ( Δt = 1 year (31,536,000 seconds) ).

2. CHI Update: [ chi_next = chi_current * r^{31,536,000} ]

Final Asset Value:

• 1,000 ESD → approximately 1,075 ESD (7.5% growth).