Hong Life CalculatorsUnderstanding the APR to APY converter — concept and principle
Savings accounts, crypto staking and loans quote rates in two ways. APR (annual percentage rate) is a simple yearly rate, while APY (annual percentage yield) includes the effect of compounding within the year. This converter turns an APR into an APY, or an APY back into an APR, for a chosen compounding frequency, and shows the rate applied in each period. Use it to compare offers that quote rates differently.
How it is calculated
With n compounding periods per year:
- APY = (1 + APR ÷ n)^n − 1
- APR = n × ((1 + APY)^(1/n) − 1)
- Rate per period = APR ÷ n
Common n values are 1 (yearly), 4 (quarterly), 12 (monthly) and 365 (daily). As n grows without limit, APY approaches e^APR − 1 (continuous compounding).
The principle
Compounding means interest earns interest. If 8% a year is paid out daily, each day adds 0.08 ÷ 365 of the current balance, and from the next day that new interest also earns. Over a year these tiny steps multiply: (1 + 0.08 ÷ 365)^365. The result is a little more than 8%. The more often interest is added, the larger the gap, but it shrinks quickly: monthly and daily compounding differ only slightly, and continuous compounding is the ceiling.
Worked example
Default: APR 8%, daily compounding.
- Rate per day: 0.08 ÷ 365 ≈ 0.0219%, shown as 0.022%.
- Compound for a year: (1 + 0.08 ÷ 365)^365 ≈ 1.0832776.
- APY = 1.0832776 − 1 ≈ 8.328%.
For comparison, monthly compounding gives about 8.300% and continuous compounding about 8.329%.
How to read the result
Compare savings or staking offers by APY, because that is what your balance actually grows by in a year if interest stays in the account. For loans, a lower APY equivalent means lower cost. If one offer quotes APR and another APY, convert one of them first. A high APY in crypto staking may also depend on token price, lock-up terms and variable rewards, which this conversion does not capture.
Common mistakes
- Comparing an APR with an APY directly.
- Assuming APY applies if interest is withdrawn each period; then you earn only the simple rate.
- Using the wrong n, for example monthly when the product compounds daily.
Frequently asked questions
What APY is 8% APR compounded daily?
About 8.33%.
Which do banks quote?
Deposit products usually show APY (in the US the Truth in Savings rules require it), while loans usually show APR.
Is APY always higher than APR?
It is higher whenever interest compounds more than once a year; with yearly compounding they are equal.
Sources: US Regulation DD (Truth in Savings), 12 CFR Part 1030, Appendix A (APY calculation) · Standard financial mathematics: effective annual rate