Effective interest rate calculator

The headline (nominal) rate says little about what a loan really costs. This calculator finds the effective annual rate as the internal rate of return of the actual payment series — the amount you receive after fees, set against the instalments you pay back. It can also convert a nominal rate with intra-year compounding into the effective annual rate. It is the mathematical effective rate, not a regulated APR figure. Everything runs in your browser; nothing is stored.

This calculator needs JavaScript because the calculation runs entirely in your browser – so your inputs never leave your device. A worked example is shown further down this page.

What your result means

The headline is the effective annual rate. In loan mode the cards also give the nominal rate for comparison, the monthly instalment and the total cost of credit (all instalments minus the net advance). The effective rate sits above the nominal rate whenever fees reduce the advance or interest compounds within the year. Treat it as the mathematical effective rate, not the figure a lender must quote under local rules.

How this calculator works

In loan mode the calculator builds the payment series: at time zero you receive the loan amount less any one-off fees (the net advance), then pay the monthly annuity instalments. The effective annual rate is the internal rate of return of that series, annualised: (1 + rₘ)^12 − 1. The internal rate is found numerically with a robustly bounded solver (Newton's method with a bisection fallback, a fixed tolerance and iteration cap); if no clear solution exists, it says so rather than inventing a figure.

Important: this is not the regulated method (the German PAngV or a statutory APR/APRC) — it is the internal rate of the payments you enter, so a lender's quoted figure can differ slightly and may include further cost components. In conversion mode it uses the closed formula effective = (1 + i/m)^m − 1, with m credits a year (1 yearly, 4 quarterly, 12 monthly).

Formula and variables

0=Net advance − Σ Instalment / (1 + rₘ)^t

Effective (loan)=(1 + rₘ)^12 − 1

Effective (conversion)=(1 + i/m)^m − 1

Net advance: loan amount less one-off fees
Instalment: monthly annuity payment at the nominal rate
rₘ: the monthly internal rate being solved for
i: nominal rate per year (conversion mode)
m: interest credits per year

Worked examples

Example: €15,000 with €450 of fees

Example inputs
Loan amount	€15,000.00
One-off fees	€450.00
Nominal rate	5.5% p.a.
Term	60 months

Example results
Effective annual rate	6.98%
Monthly instalment	€286.52
Total cost of credit	€2,641.05

The annuity instalment for €15,000.00 at 5.5% over 60 months is about €286.52 a month. Only €14,550.00 is advanced (after €450.00 of fees), so the total cost of credit is €2,641.05. The internal rate of that payment series works out to an effective annual rate of about 6.98% — well above the 5.5% nominal rate. All figures are example assumptions.

Assumptions

Regular, on-time instalments.
Fees are charged once at drawdown (your input).
No further cost components beyond what you enter.

Limitations of this calculator

Not a regulated APR/APRC or PAngV calculation — quoted figures can differ.
Real loan offers may include further costs.
No assessment of any offer or provider.

Common misconceptions

Reading it as the official APR: This is the internal rate of the payments you enter, not the regulated APR/APRC (or German PAngV) figure; a lender's quote can differ.
Comparing nominal rates only: Two loans with the same nominal rate can cost very differently once fees and compounding are included — that is what the effective rate captures.
Leaving fees out: Without the one-off fees the effective rate just reflects intra-year compounding of the nominal rate; the fees are usually what lifts it.
Expecting every cost: Real offers can carry further charges not entered here; add them as fees to get closer to the true cost.

Frequently asked questions

Is this the official APR?

No. The calculator finds the internal rate of return of the payment series you enter. That is mathematically close to the idea behind a regulated APR (or the German PAngV effective rate), but it does not reproduce the statutory method exactly, so a figure quoted in a loan contract can differ slightly.

Why is the effective rate higher than the nominal rate?

Because fees reduce the amount you actually receive while the instalments stay the same — you repay the same amount for less money, which raises the effective rate. With no fees, the effective rate is simply the nominal rate compounded within the year.

What does conversion mode do?

It turns a nominal rate with intra-year compounding into the effective annual rate using (1 + i/m)^m − 1, where m is the number of credits a year. Monthly compounding of a nominal rate gives a slightly higher effective rate than yearly.

Does it send my loan details anywhere?

No. The whole calculation happens in your browser, so the figures you enter are never stored or sent to a server.

Sources and further reading

Official and independent sources on this topic. The links open each website in a new tab; no content is loaded from them into this page.

Equivalent and Effective Interest RatesMathematics LibreTexts (Business Mathematics, J. Olivier)Reference for the effective annual rate — the true annually-compounded rate equivalent to a nominal rate compounded more often.

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Last reviewed: 28/07/2026 · All calculations run in your browser – inputs are not stored. ·How we check our calculators