Utilization and interest rates

Reading depth

Each view includes the earlier layers; the complete engineer or auditor page is shown by default.

BeginnerCore purpose and mental modelPractitionerAdds mechanisms and economicsEngineer or auditorAdds state and verification

Dependency check

Advanced detail assumes prerequisite knowledge

Before using practitioner mechanisms or engineer and auditor checks, review any unfamiliar dependency. These paths come from canonical depends_on relationships; Web3 Academy does not track completed lessons.

Review 6 dependencies

• AssetRequired through Asset versus claim

  1. Utilization and interest rates
  2. Lending pool
  3. Asset versus claim
  4. Asset

• ClaimRequired through Asset versus claim

  1. Utilization and interest rates
  2. Lending pool
  3. Asset versus claim
  4. Claim

• TokenRequired through Asset versus claim

  1. Utilization and interest rates
  2. Lending pool
  3. Asset versus claim
  4. Token

• Asset versus claimRequired through Lending pool

  1. Utilization and interest rates
  2. Lending pool
  3. Asset versus claim

• Claim tokenRequired through Lending pool

  1. Utilization and interest rates
  2. Lending pool
  3. Claim token

• Lending poolDirect prerequisite

  1. Utilization and interest rates
  2. Lending pool

Utilization compares borrowed liquidity with supplied liquidity, while a rate model maps pool state and parameters to borrower and supplier interest.

Category: LendingSplit balance category cue

System record

Start with the economic purpose, participants, resources, and entitlements before studying implementation detail.

Why it exists

Utilization-based rates price scarce pool liquidity, compensate suppliers, charge borrowers, and encourage repayment or new supply when available cash becomes low.

Traditional-finance analogy

Bank asset-liability pricing and utilization-based credit line is the closest comparison recorded for this concept.

Where the analogy stops

• Smart-contract rates can update mechanically from public state while governance, reserve factors, caps, incentives, and oracle choices still shape realized economics.
• Supplier rate and borrower rate differ because cash, reserves, fees, losses, and protocol-specific accounting sit between them.

Main actors

• ActorSupplier
• ActorBorrower
• ActorLending-pool contract
• ActorGovernance or rate administrator
• ActorReserve or incentive recipient

Assets and claims

Assets — controlled or transformed resources

Assets are resources the mechanism moves, holds, values, or transforms.

• AssetSupplied, borrowed, and available assets
• AssetAccrued interest and reserves

Claims — entitlements and corresponding dependencies

Claims are rights to value, repayment, redemption, control, or another party's performance; each depends on an obligation or system that must honor it.

• ClaimSupplier interest-bearing claim
• ClaimBorrower principal and interest obligation

Utilization compares borrowed with supplied liquidity; a rate model maps that state and configured parameters to borrower charges and supplier accrual.

Why it exists

If too much pool liquidity is borrowed, suppliers may be unable to withdraw. Rates can make scarce liquidity more expensive, encourage repayment, and attract new supply. The mechanism is an incentive and pricing rule, not a guarantee that cash will return during stress.

Traditional-finance analogy

Bank asset-liability pricing and a utilization-priced credit line are useful analogies. DeFi rates can update mechanically from public state, but governance, reserve factors, caps, incentives, bad debt, and accounting still determine what borrowers pay and suppliers actually receive.

Utilization formula, domain, and state changes

One common model is:

utilization = totalBorrowedAmount / totalSuppliedAmount

Both amounts use the same token unit, so utilization is a unitless fraction. Zero supply needs an explicit result. Protocols may exclude reserves, unbacked claims, bad debt, or other balances, so the denominator must be named rather than inferred from the contract’s token balance.

Table: Utilization formula, domain, and state changes

Pool event	Borrowed	Supplied	Utilization, all else equal
New supply	Unchanged	Rises	Falls
Withdrawal	Unchanged	Falls	Rises
Borrow	Rises	Usually unchanged	Rises
Repay	Falls	Usually unchanged	Falls
Write-off	Accounting-specific	Accounting-specific	Requires model-specific treatment

Borrow rate and supplier rate

Many models use a piecewise curve with a “kink”: the borrow rate rises gradually below a target utilization and more steeply above it. The supplier rate is not automatically the borrow rate. A simplified relationship might allocate borrower interest across utilized supply and subtract a reserve share, but exact indices, fees, compounding, and loss treatment vary.

For explicitly simple interest:

interestAmount = principalAmount × annualInterestRate × elapsedYears

annualInterestRate is a fraction such as 0.05, not 5; elapsedYears is a duration expressed in years. Production protocols often use per-second or per-block indices and compounding rather than this teaching formula.

Step-by-step rate lifecycle

1. Define which supplied, borrowed, reserved, unbacked, and written-off balances enter the utilization model.
2. Compute utilization in one token unit and handle zero supply explicitly.
3. Apply the configured rate curve, including its kink and boundary behavior, to obtain the borrower rate.
4. Accrue borrower debt over the elapsed duration under the protocol’s index and compounding rules.
5. Allocate collected interest between supplier claims, protocol reserves, and any other documented recipient.
6. Recompute utilization and rates after supply, withdrawal, borrowing, repayment, reserve, or write-off events.

Flows, payer, and loss bearer

Capital flow covers supply, borrowing, repayment, withdrawal, and realized interest payments. Claim flow grows borrower debt and supplier entitlements through the protocol’s indices, balances, or exchange rates. Return flow starts with borrower-paid interest, allocates a defined share to suppliers and reserves, and keeps token incentives from issuance or a treasury separate. Risk flow sends scarce-liquidity delays to withdrawing suppliers and can propagate underpriced credit, unexpected debt growth, or bad debt into supplier value even while the displayed rate is positive.

Engineer or auditor lens

Test zero supply, zero borrowing, utilization near and above one, kink boundaries, time gaps, per-second scaling, APR/APY conversion, compounding, index overflow, rounding, reserve allocation, repayments, write-offs, caps, and governance updates. Interest must not reduce positive borrower debt without repayment or an explicit write-off.

Compound III’s interest-rate documentation defines one pair of kinked supply and borrow models and a 10^18 utilization scale. It was reviewed 2026-08-09; its formulas, scaling, and collateral-interest behavior are not universal.

Common misunderstandings

• “90% utilization means 90% APY.” Utilization is an input to a rate model, not the rate itself.
• “Supplier APR equals borrower APR.” Available cash, reserve factors, fees, and losses sit between them.
• “A high rate guarantees withdrawals.” It may signal that available liquidity is scarce.

Continue with bad debt to see why accrued interest and collectible value can diverge.

Machine-readable model

Key equations

Canonical expressions come from the structured concept record. KaTeX renders the notation, while the plain-text expression and variable table keep its meaning and units inspectable without JavaScript. Read the narrative above for the model's domain, assumptions, and rounding rules.

1. Equation 1

   $$\mathrm{utilization} = \frac{\mathrm{totalBorrowed}}{\mathrm{totalSupplied}}$$

   Plain-text equation: utilization = totalBorrowed / totalSupplied

   Variables and units for equation 1

   Symbol	Meaning	Unit
   utilization	Utilization	dimensionless fraction (1 = 100%)
   totalBorrowed	Total Borrowed	selected underlying-asset units
   totalSupplied	Total Supplied	selected underlying-asset units

2. Equation 2

   $$\mathrm{simpleInterest} = \mathrm{principal} \times \mathrm{annualInterestRate} \times \mathrm{elapsedYears}$$

   Plain-text equation: simpleInterest = principal * annualInterestRate * elapsedYears

   Variables and units for equation 2

   Symbol	Meaning	Unit
   simpleInterest	Simple Interest	selected underlying-asset units
   principal	Principal	selected underlying-asset units
   annualInterestRate	Annual Interest Rate	fraction per year (1 = 100% per year)
   elapsedYears	Elapsed Years	years

Assurance contract

Security properties

These structured statements define desired behavior. Their stable IDs can bind tests, invariants, specifications, audit findings, or proof results without turning descriptive review advice into an assurance claim.

Desired · not evaluated: No test, audit, or proof result is implied until scoped evidence is linked to this property.

1. SP-01Desired · not evaluated

   Utilization and rates state numerator, denominator, units, domain, scaling, and zero-supply behavior

2. SP-02Desired · not evaluated

   Interest accrual never reduces positive borrower debt absent repayment or explicit write-off

3. SP-03Desired · not evaluated

   Supplier claims, borrower debt, reserves, and protocol fees reconcile after accrual

4. SP-04Desired · not evaluated

   APR, APY, compounding, incentives, reserve factors, and realized returns remain separately labelled

Prerequisites

Direct dependencies recorded by this concept's canonicaldepends_on relationships.

• Lending poolPath 16

  A lending pool aggregates supplied assets, issues supplier claims, and makes available liquidity borrowable under interest and risk rules.

Learn next

Concepts that directly depend on this one, ranked by the recommended learning path. Check each page for additional prerequisites.

No concept directly builds on this page in the current graph; use the guided learning paths to choose another branch.

Knowledge check

Quiz

Answer in your own words, then open the model answer.

What problem does Utilization and interest rates exist to address?

Model answer

Utilization-based rates price scarce pool liquidity, compensate suppliers, charge borrowers, and encourage repayment or new supply when available cash becomes low.

Mark as understood