APR, APY and Supplier Yield Are Different Numbers
The $USDT reserve interface labels its borrowing quotation “APY, variable,” while its rate-model chart uses variable borrow APR.
**Variable borrow APR** is the annualized rate used in the debt-accrual calculation, before expressing the effect of compounding. It is not a fixed quote for the loan’s duration.
**Borrow APY** expresses an annualized compounded cost assuming the quoted rate stays unchanged. Aave’s rate-formatting code converts APR using a per-second compounding convention: `(1 + APR / seconds per year)^(seconds per year) − 1`. It is a comparison measure, not a forecast of the borrower’s eventual bill.
**Supplier yield** is the return to the other side of the reserve, not the borrower’s interest rate. The deployed rate strategy calculates the liquidity rate from the borrow rate, the supply utilization ratio and the portion retained through the reserve factor. The $USDT interface showed a 10% reserve factor when checked on Oct. 28. That is a share of interest, not an extra 10% charge on the borrower’s principal.
Liquidity connects the two sides. More borrowing relative to available liquidity can raise the rate; withdrawals can also tighten the reserve. The Defiant’s report on a wallet moving 150 million $USDT from Aave to Spark Savings describes that liquidity context. Its Aave–Bitso lender comparison addresses the separate question of what suppliers hold and what limits their exits.
Following One Loan Across a Rate Change
Aave does not calculate variable debt simply as original principal multiplied by the latest APR and elapsed time. Its debt token applies a growing reserve-wide **borrow index** to the borrower’s scaled balance. With no further borrowing or repayments, the scaled balance stays unchanged while the amount owed grows.
The Ethereum Pool and $USDT debt-token implementations checked on Oct. 28, 2026 use compounded debt accrual. For each interval between reserve updates, the Pool approximates the growth factor as `1 + x + x²/2 + x³/6`, where `x = APR × elapsed seconds / (365 days)`. Successive index updates multiply those factors. This contract calculation is distinct from the APY display convention.
Consider a **hypothetical 10,000-$USDT loan**: 30 days at 4.5% APR, followed by 30 days at 7% APR. Assume no repayments, additional borrowing or liquidation, with a reserve-index update at the rate-change boundary and no intermediate updates within either interval. These are illustrative rates and timing, not a reconstruction of an actual account.
Using the deployed formula, and rounding the results to two decimals:
– **After the first 30 days:** approximately **37.05 $USDT** of interest has accrued, making the debt **10,037.05 $USDT**. – **At the rate change:** the debt remains approximately **10,037.05 $USDT**. The original amount borrowed is still **10,000 $USDT**; the existing interest is not erased or recalculated at 7%. – **After the next 30 days:** approximately **57.91 $USDT** more interest has accrued on the growing debt. The balance is approximately **10,094.97 $USDT**, comprising **10,000 $USDT borrowed plus 94.97 $USDT in accumulated interest**.
These are The Defiant’s illustrative calculations, using unrounded intermediate balances. Actual balances depend on the sequence of rates, reserve-update times and contract rounding. The deployed $USDT debt-token implementation derives the amount owed from the scaled balance and current borrow index, rounding the resulting debt upward to the token’s smallest unit.
