The Complete Guide to Converting APR and APY
By Arshi Khan, Founder of Just4Marketing · Last reviewed October 2026
APR and APY describe the same interest rate in two ways: APR leaves out compounding and APY includes it. Savings accounts usually quote APY, while loans and credit cards quote APR, so converting one into the other is the only way to compare offers fairly. This guide gives both formulas, shows how compounding frequency changes the result, and explains when each number matters.
The formulas
APY = (1 + APR ÷ n)n − 1, and APR = n × ((1 + APY)1/n − 1), where n is the number of times interest compounds each year. For continuous compounding, APY = eAPR − 1 and APR = ln(1 + APY).
The rate per period is simply APR ÷ n. A 5% APR compounded monthly charges or pays 0.417% each month.
How compounding frequency changes APY
| 5% APR compounded | APY |
|---|---|
| Annually | 5.000% |
| Semi-annually | 5.062% |
| Quarterly | 5.095% |
| Monthly | 5.116% |
| Weekly | 5.125% |
| Daily | 5.127% |
| Continuously | 5.127% |
$10,000 at a 5% APR compounded monthly grows to $10,511.62 after one year — exactly 5.116% more, which is the APY.
When to use each number
Savings, CDs and deposits
Compare APY with APY. It shows what you actually earn in a year if you leave the interest in.
Credit cards
Cards quote APR, but interest compounds. Convert to APY to see the real yearly cost of a balance you carry.
Loans and mortgages
Compare APR with APR for overall cost, since it may include fees; use the interest rate for the payment.
Crypto staking
A quoted APY usually assumes you restake rewards at a set frequency. If you won't, the APR is closer to what you'll earn.
Frequently asked questions
How do I convert APR to APY?
Use APY = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods a year. A 5% APR compounded monthly is (1 + 0.05 ÷ 12)^12 − 1 = 5.116% APY.
How do I convert APY to APR?
Reverse the formula: APR = n × ((1 + APY)^(1/n) − 1). A 4.5% APY compounded monthly equals an APR of about 4.410%; compounded daily, about 4.402%.
Is APY always higher than APR?
When interest compounds more than once a year, yes. With yearly compounding the two are equal. The more often interest compounds, the bigger the gap, though the difference between daily and continuous compounding is tiny.
Does a loan's APR include fees?
On many loans, especially mortgages, the advertised APR includes certain lender fees spread over the loan's life, so it can be higher than the interest rate used to set your payment. This calculator converts a pure rate; it doesn't add or remove fees.