how annual percentage rate works

What Is Annual Interest Rate?

The annual interest rate represents the cost or return on funds expressed as a yearly percentage, making it easier to compare products with different interest calculation periods. It is commonly used in savings, loans, exchange-based financial products, and DeFi.

Intuitively, the annual interest rate acts as a "price tag": for borrowing, it’s a cost indicator; for saving, it’s a yield indicator. Seeing the annual interest rate standardized across products allows for informed comparisons.

Why Is Annual Interest Rate Important?

Annual interest rate is essential because it unifies various rates—such as daily and monthly rates—onto a common scale for easier comparison and decision-making. For borrowers, it reflects total costs; for investors, it shows true returns.

In recent years, traditional savings have had relatively low annual interest rates, while returns in financial products and DeFi can vary widely. Using annualized rates enables objective evaluation of risk-reward profiles.

How Is Annual Interest Rate Calculated?

There are two main calculation methods: APR (Annual Percentage Rate), which does not include compounding, and APY (Annual Percentage Yield), which does. APR is more straightforward; APY reflects the actual compounding effect.

• APR calculation: APR = Periodic Rate × Number of Periods per Year. For example, if the monthly rate is 1% and there are 12 months, APR = 1% × 12 = 12%.
• APY calculation: APY = (1 + Periodic Rate)^(Number of Periods per Year) – 1. For a monthly rate of 1%, APY = (1 + 0.01)^12 – 1 ≈ 12.68%.

Example: Principal of 10,000 units, monthly rate of 1%:

• Using APR (no compounding): Annual interest = 10,000 × 1% × 12 = 1,200 units.
• Using APY (with compounding): Annual balance = 10,000 × (1 + 0.01)^12 ≈ 11,268 units; interest ≈ 1,268 units.

Another example: With a daily rate of 0.02%, APY ≈ (1 + 0.0002)^365 – 1, resulting in a range of about 7% to 8%, depending on the exact number of days and whether interest compounds daily.

If there are fees or annual charges, these should be included in the cost to calculate the "effective annualized cost." For example, if you borrow 10,000 units with a nominal annual interest rate of 10% and a one-time fee of 2% (200 units), the actual annualized cost will exceed 10%. It can be approximated as (interest + fees) / net amount received.

What’s the Difference Between APR and APY?

APR is the annual rate without compounding—think “how much percentage is added each year.” APY factors in compounding—representing “the total compounded return over a year.”

When interest is settled frequently (daily or monthly) and reinvested, APY is typically higher than APR. If there is no reinvestment or only one settlement at term-end, the rates are similar. If only APR is shown on a product page, users can convert it to APY using the formula for a more accurate annualized yield.

How Is Annual Interest Rate Used in Savings and Loans?

For savings, annual interest rate helps compare products with different terms and frequencies. Pay attention to whether the rate shown is APR or APY, if compounding applies, early redemption options, and relevant interest rules.

For loans, annual interest rate measures total borrowing costs. Consider not just nominal APR but also additional fees (annual fees, management charges, handling fees) and whether these are included in the effective annualized cost. Be aware of differences caused by floating rates and repayment methods (fixed principal and interest vs. fixed principal).

Credit cards often charge interest daily and impose annual fees. If balances roll over, actual annualized costs can rise sharply—avoid long-term debt whenever possible.

How Is Annual Interest Rate Calculated in DeFi?

Annual interest rates in DeFi typically apply to staking (locking tokens for rewards) and liquidity pools (depositing pairs or groups of tokens for trading fees and incentives). Platforms may display either APR or APY.

On Gate’s financial and staking pages, products are usually marked with APR or APY. If only APR is shown but rewards are settled daily, users can estimate APY using: APY = (1 + APR/365)^365 – 1. If auto-compounding is supported, APY will closely match this formula.

Example: A stablecoin pool offers an APR of 8%. With daily compounding, estimated APY ≈ (1 + 0.08/365)^365 – 1, slightly above 8%. Without reinvestment or with irregular rewards, actual APY may be lower than calculated.

In liquidity pools, earnings come from both trading fees and token rewards—these fluctuate with trading volume and incentive programs. Displayed annual rates are often estimates; users should adjust for compounding frequency and method.

What Are the Steps to Calculate Annual Interest Rate?

Calculating annual interest rate involves a series of steps to ensure consistent and comparable results:

1. Identify whether the product displays APR or APY and whether reinvestment is allowed or automated.
2. Determine the interest calculation frequency (daily, monthly, per block) and periodic rate.
3. Convert periodic rate to annualized terms: if no compounding, use APR = periodic rate × number of periods; if compounding applies, use APY = (1 + periodic rate)^(number of periods) – 1.
4. Include fees or annual charges: For loans, estimate effective annualized cost using total cost/net funds received; for investments, use net return/invested capital to annualize returns.
5. For floating rates, estimate across intervals—set optimistic, base-case, and conservative scenarios for sensitivity analysis.
6. Record product term length and liquidity features (early withdrawal options or penalties) to avoid misjudging returns due to liquidity restrictions.

What’s the Difference Between Fixed and Floating Annual Interest Rates?

Fixed annual interest rates remain unchanged for the entire term—making planning easier. Floating rates fluctuate with market conditions or protocol parameters—resulting in less certainty about returns or costs.

For loans, fixed rates ensure stable repayments; floating rates may increase costs if market rates rise. In DeFi, floating annual rates are common—affected by supply-demand dynamics, trading volume, and changing incentives—users should model scenarios for risk control.

What Risks Should You Watch Out For With Annual Interest Rates?

Risks related to annual interest rates include rate fluctuations, early redemption penalties, miscalculations due to excluded fees, inflation eroding real returns, tax implications, and platform or protocol security vulnerabilities.

In DeFi and exchange financial products, pay attention to smart contract bugs, changes in reward structures, asset price volatility, and impermanent loss. Before using Gate’s financial or staking services, always review product documentation and terms—confirm calculation methods, fees, redemption rules—and follow the outlined steps to accurately assess returns and risks.

Annual Interest Rate Key Takeaways

The annual interest rate is essential for consistently comparing funding costs and returns across products. Understanding the differences between APR and APY, how compounding frequency affects yields, and accounting for fees helps avoid common pitfalls. Whether saving, borrowing, or investing through Gate’s financial or DeFi offerings—always identify how rates are presented, apply proper annualization steps including fees and liquidity constraints, then weigh risk relative to your goals. For floating rates especially, estimate ranges to maintain safety margins and flexibility.

FAQ

How much is an annual interest rate of 0.4% ("4 li")?

An annual interest rate of "4 li" equals 0.4%. The calculation: Interest = Principal × 0.4%. For example, with a principal of 100,000 units at a "4 li" rate, one year’s interest equals 100,000 × 0.4% = 400 units. This is relatively low and typically found in bank savings accounts or some investment products.

How much interest does 100,000 units earn in a bank account over one year?

It depends on the specific annual interest rate. For regular savings accounts (around 0.3%), one year’s interest would be about 300 units; for fixed-term deposits (about 1.5%-3%), one year’s interest ranges from 1,500 to 3,000 units. The formula: Interest = Principal × Annual Interest Rate—the type of deposit directly impacts final earnings.

Which yields more: an annual rate of 2% or "4 li"?

A 2% annual rate yields significantly more. Two percent equals "200 li," which is about 50 times higher than "4 li" (0.4%). For a principal of 100,000 units: at 2%, one year earns 2,000 units; at "4 li," only 400 units. With equal principal amounts, higher annual rates always generate more interest.

How are principal amount and calculation periods determined in interest calculations?

The principal is the amount actually deposited or borrowed; the calculation period refers to how often interest accrues. Different institutions have different standards: banks usually calculate daily or monthly; crypto lending platforms like Gate may calculate hourly or daily. Both factors are crucial—shorter cycles mean greater compounding effects and different final returns.

How do you convert between daily/monthly/annual interest rates?

The conversion relationships are: Annual Rate = Monthly Rate × 12 = Daily Rate × 365 (approximate). For example: a daily rate of 0.01% converts to an annual rate of roughly 3.65%. When comparing rates across different periods, it’s best to standardize as annual rates for clear comparison—avoid being misled by figures shown in other timeframes.