Annual Interest ↔ Monthly Interest Rate Converter
Convert between annual, monthly, and daily interest rates — for both simple and compound interest. Understand APR vs APY and the true cost of any loan or return on any deposit.
APR vs APY — Why They’re Different
APR (Annual Percentage Rate) is the simple annual rate — just multiply the periodic rate by the number of periods. APY (Annual Percentage Yield) accounts for compounding — the interest earns interest. For a 1% monthly rate: APR = 12%, but APY = (1.01)^12 − 1 = 12.68%. That 0.68% difference costs $6,800 extra interest per $10 hundred thousand per year.
Banks quote FD rates as APY (higher, looks better) but quote loan rates as APR (lower, looks cheaper). Always ask: “Is this the APR or APY?”
Monthly Rate (compound) = (1 + Annual Rate)^(1/12) − 1
APY = (1 + APR/n)^n − 1 [n = compounding periods per year]
APR from monthly rate = Monthly Rate × 12
APY from monthly rate = (1 + Monthly Rate)^12 − 1
Bank A APY: (1+0.072/4)^4 − 1 = 7.40%
Bank B APY: (1+0.07/12)^12 − 1 = 7.23%
Bank A is better despite appearing to have a lower compound frequency!
💡 What This Means for You
For credit card debt at 3% per month: APR = 36%, but APY = (1.03)^12 − 1 = 42.6%. This is why carrying a credit card balance for even a few months becomes extremely expensive. Pay off credit card balances in full every month.
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