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. The contractual APR published by a lender incorporates the nominal interest rate, the compounding frequency and the mandatory fees and charges of the operation; 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). The result is therefore the mathematically equivalent APR derived from the nominal rate and the compounding frequency. It does not calculate the full contractual APR of a loan or mortgage when fees, charges or other costs apply. To compare real offers, use the APR published by the lender.
Mathematical equivalent APR (by compounding)
5,1162%
With monthly (12 times/year) compounding, a nominal rate of 5% equals an APR of 5,1162%
The nominal-rate↔APR conversion results are mathematically exact, but they only reflect the effect of compounding. A loan's contractual APR is usually higher because it also incorporates mandatory fees and charges, which this tool does not include.
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.
How to compare two loan offers without getting it wrong
Picture two €10,000 loans over five years. The first offers 6% nominal with no fees. The second, 5.5% nominal with a 2% arrangement fee and compulsory insurance at €15 a month. At first glance the second wins, but the fee is €200 paid up front and the insurance adds €900 over the life of the loan, so its real cost is clearly higher. That is exactly the information the APR summarises, and why it is the only figure comparable between lenders. Three cautions when using it. First: the APR only includes costs that are compulsory to obtain the loan, so insurance sold as voluntary but conditioning the rate may fall outside it. Second: always compare the same term, because stretching it lowers the payment and raises the total cost. And third, look at the total amount owed shown in the pre-contractual information: that is the figure that actually leaves your pocket.