Nominal vs effective: why the two numbers differ
A nominal annual rate is the headline number on a loan or savings account — for example, 12% per year. The effective annual rate (often called APY for deposits, EAR for loans) is what you actually earn or owe once compounding is factored in. Compound the same 12% monthly instead of once a year and the effective rate becomes 12.6825% — you earn interest on interest twelve times per year instead of once.
The formula is straightforward: EAR = (1 + r/n)^n - 1, where r is the nominal annual rate and n is the number of compounding periods per year. As n grows toward infinity (continuous compounding), the formula collapses to EAR = e^r - 1.
Why it matters when you read a bank statement
Most consumer credit-card statements quote a nominal APR but actually charge interest daily. A 19.99% nominal APR compounded daily lands at 22.13% effective — the gap is real cash you owe. Mortgages in the EU usually publish the effective rate (TAEG / AER) by law so consumers can compare apples to apples; US statements still default to nominal APR.
If you're reconciling a credit-card or revolving-credit statement in our main converter, paste the issuer's nominal APR here first to sanity-check the actual interest charge line.
The five compounding frequencies you'll see in the wild
- Annually (1×): Old-school savings bonds and most EU government-issued retail bonds. Effective = nominal.
- Semi-annually (2×): Most US Treasuries and many corporate bonds. A 6% nominal becomes 6.09% effective.
- Quarterly (4×): Common on EU business-loan and fixed-deposit products. A 6% nominal becomes 6.136% effective.
- Monthly (12×): Mortgages, personal loans, most savings accounts. A 6% nominal becomes 6.168% effective.
- Daily (365×) or continuous: Credit cards and some money-market funds. A 6% nominal becomes ~6.183%. The gap between daily and continuous is tiny — under 0.001 pp.
Reading the results
- Effective annual rate: the number to compare across products. Always use this — never compare a nominal rate to an effective one.
- Per-period rate: what each compounding step actually applies. Useful for verifying line items on a statement (the monthly interest line on a credit card, for instance).
- Time to double: exact closed-form value of
ln(2) / ln(1 + EAR). The rule-of-72 approximation is within a few months for rates between 4% and 12%. - Future value: simple compounding —
P × (1 + EAR)^years. No deposits, no withdrawals. For more complex cashflows, you want an annuity calculator.
What this calculator does not do
We compute pure compound-interest figures. We do not model ongoing deposits or withdrawals (annuities), tax drag, inflation, or amortising loan schedules with fees. If you need an amortisation schedule for a mortgage, a dedicated mortgage calculator from your bank or central bank will be more honest about front-loaded interest.
For analysing actual statement transactions and verifying the interest charged matches the published rate, drop your statement PDF into our bank statement converter first — get the transactions into a spreadsheet, then come back here to cross-check the rate math.