Startseite › Glossar › Annuity Instalment (Annuität)
Glossar · Finance
Annuity Instalment (Annuität)
A constant payment over a loan's fixed-rate period that combines interest and principal — the standard form of Austrian and German mortgage loans, prized for its predictability.
Concept
The Annuität (annuity instalment) is a constant payment over the entire term of a loan, comprising both interest and principal repayment. The term derives from the Latin annuus (yearly), but today it is usually applied monthly — strictly speaking the proper label would then be monthly annuity payment.
The annuity loan is the most common form of mortgage loan in Austria and Germany. It combines maximum predictability of the monthly burden with an automatic acceleration of principal repayment over time.
The maths
The annuity A follows the standard formula:
A = K × (i × (1 + i)^n) / ((1 + i)^n − 1)
where K = loan amount, i = period interest rate (e.g. monthly), n = number of periods.
Example: a €250,000 mortgage at 4.0% per year nominal over 25 years generates a monthly annuity of around €1,319. Over the full term the borrower pays roughly €395,700 — €250,000 of principal and €145,700 of interest.
How the mix evolves
In the first month of the example above, about €833 goes to interest (4.0% per year on €250,000 divided by 12) and only €486 to principal. With each instalment, the residual debt drops slightly, the interest share falls and the principal share rises accordingly.
After 10 years, the principal share is already around €730 and interest only €589. In the final year of the term, the monthly instalment consists almost entirely of principal.
This dynamic explains why extra repayments in the early years save disproportionately more interest — they cut residual debt early, with a cumulative effect over the remaining term.
Annuity in actuarial and financial mathematics
Outside the lending context, annuity also refers to a regular constant payment over a limited period — a pension stream from a life-insurance contract, a contribution into a savings plan or an annual ground-rent payment. The concept of present value is derived from this generalisation: today's equivalent of a stream of future annuities, discounted at a given rate.
In the pension-fund and life-insurance context, the "lifetime annuity" is the guaranteed monthly payout until death — its amount depends on entry age, gender, guarantee rate and mortality tables.