Also known as: Annuity payment, Level payment
Annuity
A series of regular payments of the same size at equal intervals. On a loan it is the instalment that never changes for the whole of the repayment.
An annuity is a payment that stays the same size throughout. That is what lets you know exactly what to budget for. The only thing that changes is what is inside it: at the start most of it goes to interest, and progressively more of it to the debt itself.
Why the split changes
Interest is calculated on the balance outstanding. At the start the balance is at its highest, so interest eats most of the instalment and little is left to reduce the debt. As the debt falls, so does the interest on it, and an instalment of the same size clears an ever larger part of the principal.
That gradual shift in the ratio is called amortisation. It is exactly why, in the first years of a mortgage, the debt seems barely to move.
The formula
The annuity instalment is set precisely so that the last payment brings the debt to zero:
- : the size of one instalment
- : the principal borrowed
- : the interest rate for one period (the annual rate divided by twelve)
- : the total number of instalments
The formula comes from discounting: the loan equals the sum of all future instalments restated in today's money.
A worked example
You borrow €200,000 at 4% a year over 25 years.
The monthly instalment works out at €1,055.67. Over the whole term you pay the bank €316,702, of which €116,702 is interest.
In the first instalment €666.67 goes to interest and only €389 to the principal. In the last one it is exactly the other way round.
Types of annuity
- Ordinary annuity
Payments fall at the end of each period. This is how mortgages and most consumer loans work.
- Annuity due
Payments fall at the start of the period, typically rent or insurance premiums. On the same terms it has a higher present value, because every payment earns interest for one period longer.
What to watch out for
A lower monthly instalment almost always means paying more in total. Extending the term from 20 to 30 years lowers the instalment, but the interest you pay is substantially higher: deciding on the monthly figure alone is the most common mistake.
Where you will meet it
The annuity sits behind mortgage and loan repayment, pension payouts, leasing and insurance settlements. The same principle in reverse, regular contributions instead of instalments, drives saving with compound interest.
Test your own figures in the mortgage calculator, including the amortisation table and the effect of overpayments.