# Lending interest indexes: accruing balances without daily transfers A lending interest index accumulates a rate over time so a protocol can derive current balances from stored scaled balances. Supply and debt can use different indexes and formulas. The result depends on the implementation, elapsed time and rate changes; it is not a promise of a fixed annual return. Evidence: [Aave V3 ReserveLogic](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/logic/ReserveLogic.sol); [Aave V3 MathUtils](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol) Canonical: https://degreesofsatoshi.com/encyclopedia/money-market-interest-indexes/ Published: 2026-10-02 Substantively modified: 2026-10-02 Independently verified by an automated reviewer: 2026-10-02T18:15:18.493Z Data current through: 2026-10-02 AI-assisted research and drafting with a separate automated source-verification pass; no external expert or named human review is implied. ## Key facts - **Supply:** Aave’s cited implementation exposes normalized income through a liquidity index. ([Aave V3 ReserveLogic](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/logic/ReserveLogic.sol)) - **Debt:** Variable debt uses a separate cumulative borrowing index. ([Aave V3 ReserveLogic](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/logic/ReserveLogic.sol)) - **Formula:** The cited MathUtils uses linear interest and an approximation for compounded interest. ([Aave V3 MathUtils](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol)) ## Multiply a scaled balance by its index Ignoring fixed-point scale and rounding, a scaled balance of 100 at an index of 1.02 corresponds to 102 underlying units. If the index later becomes 1.03, the balance reads as 103. The actual contracts use large integer scale factors and specified rounding. The decimal example explains the relationship without reproducing every implementation detail. Evidence: [Aave V3 ReserveLogic](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/logic/ReserveLogic.sol) ## Accrual does not require a payment transaction per holder A balance query can incorporate the latest index even though no ordinary transfer event paid interest to that holder each second. State updates and normalized calculations handle the accumulated amount. An explorer’s transfer list is therefore not always sufficient to reconstruct an interest-bearing token’s current balance. Evidence: [Aave V3 ReserveLogic](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/logic/ReserveLogic.sol); [Tokenization](https://aave.com/docs/aave-v3/smart-contracts/tokenization) ## Use the formula for the deployed version This example cites aave-v3-core v1.19.3, an explicitly versioned implementation. It is not a claim that every present deployment uses identical math. For a calculation at a block, record the reserve index, last update time, relevant rate and version. A dashboard APR alone may not reproduce the exact integer balance. Evidence: [Aave V3 MathUtils](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol); [Aave V3 ReserveLogic](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/logic/ReserveLogic.sol) ## Questions ### Does interest appear only when someone sends me new tokens? Not necessarily. An indexed token can calculate a growing balance from its stored scaled amount and a cumulative index, without a separate ordinary transfer for each accrual interval. Evidence: [Tokenization](https://aave.com/docs/aave-v3/smart-contracts/tokenization); [Aave V3 ReserveLogic](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/logic/ReserveLogic.sol) ## Claims and scope ### money-market-interest-indexes-quick-answer A lending interest index accumulates a rate over time so a protocol can derive current balances from stored scaled balances. Supply and debt can use different indexes and formulas. The result depends on the implementation, elapsed time and rate changes; it is not a promise of a fixed annual return. Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null} ### money-market-interest-indexes-fact-supply Supply: Aave’s cited implementation exposes normalized income through a liquidity index. Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null} ### money-market-interest-indexes-fact-debt Debt: Variable debt uses a separate cumulative borrowing index. Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null} ### money-market-interest-indexes-fact-formula Formula: The cited MathUtils uses linear interest and an approximation for compounded interest. Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null} ## Sources - [Aave V3 ReserveLogic](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/logic/ReserveLogic.sol) — Aave. Cumulative supply and borrow indexes update accounting over time. Locator: getNormalizedIncome; getNormalizedDebt; updateState. Retrieved: 2026-10-02T17:03:44.467Z. - [Aave V3 MathUtils](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol) — Aave. Protocol-specific simple and approximated compounded interest calculations. Locator: calculateLinearInterest; calculateCompoundedInterest. Retrieved: 2026-10-02T17:03:44.337Z. - [Tokenization](https://aave.com/docs/aave-v3/smart-contracts/tokenization) — Aave. Supply receipt and nontransferable debt accounting using interest indexes. Locator: aToken; VariableDebtToken. Retrieved: 2026-10-02T17:03:44.686Z. ## Revision history - 2026-10-02: First publication after primary-source research and independent automated verification. ## Cite this entry Degrees of Satoshi editorial project. “Lending interest indexes: accruing balances without daily transfers.” Published 2026-10-02; updated 2026-10-02. https://degreesofsatoshi.com/encyclopedia/money-market-interest-indexes/