Number format: this calculator uses German notation throughout — a comma is the decimal separator and a dot groups thousands. “1.234,56” means one thousand two hundred thirty-four euros and fifty-six cents. The figures come from German tax law, so they are shown the way German authorities write them.
Effective annual rate (effektiver Jahreszins)
The rate that includes every cost — the honest figure for comparing loans.
In plain language
The nominal rate (Sollzins) only says what the bank charges for the money it lends. The effective annual rate says what the loan costs in total — including arrangement fees, the timing of the instalments and any compulsory payment protection insurance. That makes it the only figure with which you can genuinely compare two offers: a loan at 3,0 % nominal with high fees can be dearer than one at 3,3 % with none.
In detail
The effective annual rate is the internal rate of return of the payment series: the rate at which the present value of all payments (drawdown, instalments, fees, final payment) comes to exactly zero. The formula is set out in the annex to § 16 PAngV 2022; the result must be stated to two decimal places. Because the equation cannot be rearranged for the rate, it is solved numerically (Newton's method with a bisection fallback). Unlike the nominal rate it accounts for WHEN payments fall — a fee at the start weighs more than the same sum at the end.
Worked example
A 10.000 € loan repaid with 11.000 € after one year: 10,00 % effective. If the bank withholds a 100 € arrangement fee up front, only 9.900 € is paid out — with the same repayment the effective rate rises to 11,11 %, although the nominal rate looks unchanged. That difference is exactly what the effective rate makes visible.
In brief
Iterative solution of the present-value equation over the actual series of payments, not an approximation. Fees and discount are included.
Legal basis: § 16 PAngV and its annex · as at 2026