APR / Nominal Rate Converter
Convert between nominal interest rate (TIN) and APR (Annual Percentage Rate) based on the compounding frequency. Essential for comparing mortgages, loans and deposits.
The APR (Annual Percentage Rate) is the indicator that allows homogeneous comparison of different financial products, as it incorporates not only the nominal interest rate, but also the compounding frequency and fees. It is the figure that, by law, financial institutions must display prominently in their advertising for loans, mortgages and deposits.
This calculator converts in both directions between the nominal rate and APR using the standard formula: APR = (1 + nominal/n)^n − 1, where n is the annual compounding frequency. It also generates a comparison table to visualise how the APR varies by frequency (daily, weekly, monthly, quarterly, half-yearly or annual), which is particularly useful for understanding the true cost of a loan.
Equivalent APR
5,1162%
With monthly (12 times/year) compounding, a nominal rate of 5% equals an APR of 5,1162%
Results are mathematically exact. The actual APR of a loan may differ if it includes additional fees not considered here.
How the APR is calculated from the nominal rate
The formula relating the two indicators is APR = (1 + nominal/n)^n − 1, where n is the number of times interest is compounded in a year. The logic is simple: if interest is credited several times a year, the amounts generated in each period start earning interest themselves for the rest of the year, so the effective return exceeds the advertised nominal rate. When compounding is annual (n = 1) the formula simplifies and APR and nominal rate coincide. As n grows, the APR rises, though ever more slowly as it approaches a mathematical limit.
Worked example
Take a nominal rate of 6% with monthly compounding, that is, n = 12. Applying the formula: APR = (1 + 0.06/12)^12 − 1 = (1 + 0.005)^12 − 1 = 1.061678 − 1 = 0.061678, i.e. 6.17%. The 0.17 percentage point difference seems small, but on €200,000 over thirty years it translates into several thousand euros. If compounding were quarterly (n = 4), the APR would be 6.14%; if annual, it would match the 6% nominal rate exactly.
APR resulting from a 6% nominal rate by compounding frequency
| Frequency | APR |
|---|---|
| Annual | 6,00 % |
| Half-yearly | 6,09 % |
| Quarterly | 6,14 % |
| Monthly | 6,17 % |
| Daily | 6,18 % |
How to interpret the result
The APR is the only indicator the law requires to be published precisely so you can compare products across lenders on equal terms, so always use it as your main criterion. That said, two limits are worth remembering. First, a lower APR does not always mean the cheapest product in your particular case: if you plan to repay early, the distribution of fees may matter more than the rate. Second, in mortgages the APR leaves out linked insurance, which can raise the real cost considerably; to compare properly, always ask for the full amortisation schedule and add the annual cost of any products you are required to take out.