How do DeFi lending apps set interest rates?

Utilisation

Compound's documentation gives the formula: utilisation = total borrowed ÷ total supplied.¹ Aave describes the utilisation rate as the share of supplied money in a pool that is borrowed.²

So a pool with $10 million supplied and $6 million borrowed has a utilisation of $6 million ÷ $10 million = 60%.¹

Why the rate follows utilisation

Aave's risk documentation explains the logic.⁴

• When there is plenty of money in the pool, rates are low, to encourage borrowing.⁴
• When money is scarce, rates are high, to encourage borrowers to repay and lenders to supply more.⁴

This matters because lenders can only take out what is not lent out. Aave says lenders can withdraw as long as there is enough unborrowed money in the pool.² It says rising rates help make sure enough remains for withdrawals and liquidations.⁵

The kinked curve

Aave's V3 model has two slopes around an "optimal" utilisation point. Below that point, the borrow rate rises with the first slope. Above it, the rate rises faster, with the second slope.³ Compound calls the bend a "kink": above it, the rate increases more rapidly.¹

Aave's risk documentation writes the model like this.⁴

• Up to the optimal point: rate = base rate + (utilisation ÷ optimal utilisation) × slope 1.⁴
• Above it: rate = base rate + slope 1 + ((utilisation − optimal) ÷ (100% − optimal)) × slope 2.⁴

Each pool has its own numbers, set through governance.^5,1 Aave's risk documentation says that when a pool is fully lent out, its rates rise sharply, to above 50% a year.⁴

Variable rates

Most DeFi loans have a variable rate. Aave's risk documentation says the rate on variable debt keeps changing with utilisation.⁴ So the rate you see when you borrow is not a promise.²

Interest is added all the time. Compound says interest accrues every second.¹ On Aave, a borrower's debt is tracked by tokens that grow as interest builds up.³

Compound turns its per-second rate into a yearly rate, the APR, by multiplying by the number of seconds in a year.¹ Aave's glossary explains the difference between APR and APY: APY includes compounding, and APR does not.⁶ Module 21 covers APR, APY and yield in more detail.

What lenders earn

Lenders are paid from borrowers' interest, minus the reserve factor that goes to the protocol.^3,6 So lenders earn a lower rate than borrowers pay. Only part of the pool is lent out, and part of the interest is kept back.^3,1

Some designs treat collateral separately. In Compound III, collateral earns no interest at all; only the main asset that is lent and borrowed does.¹