Actuarial rate
An actuarial rate is an annual interest rate computed using compound-interest mathematics, discounting all cash flows — repayments and fees — over the exact loan term. It contrasts with the proportional rate and serves as the legal basis for the APR in France.
Key points
- Based on compound interest: each period capitalizes previously accrued interest.
- Mandatory for APR computation under the EU Mortgage Credit Directive (2014/17/EU).
- Different from the proportional rate: 1% per month ≠ 12% actuarial (gap of roughly 0.07 points).
- Enables consistent comparison between offers with different payment frequencies (monthly, quarterly).
- Used by notaries for calculating late-payment interest and compensation amounts.
Frequently asked questions
Why is the actuarial rate used instead of the proportional rate for the APR?
The actuarial method reflects the economic reality of compounding: every euro paid late itself generates further interest. The proportional rate, obtained by simply dividing the annual rate by the number of periods, understates this effect. EU lawmakers therefore mandated the actuarial method to ensure honest disclosure of the true cost of credit.
How do you convert a monthly rate to an annual actuarial rate?
Apply the compounding formula: annual actuarial rate = (1 + monthly rate)^12 − 1. For example, a monthly rate of 0.25% yields an annual actuarial rate of approximately 3.04%, not 3.00% as the proportional method would produce.
What is the difference between the actuarial rate and the nominal rate?
The nominal rate is the raw contractual rate the bank advertises, without accounting for payment frequency. The actuarial rate incorporates compounding to produce a strictly comparable annual figure. In practice, for monthly payments, the actuarial rate is slightly higher than the nominal rate.
In practice
A broker compares two offers: 3.20% monthly proportional and 3.15% annual actuarial. Converting the first to actuarial terms gives 3.27%, revealing that the offer quoted on an actuarial basis is actually 0.12 points cheaper — roughly €3,200 in savings on €250,000 over 20 years.
Official sources
- The annual percentage rate (APRC) · Service-Public.gouv.fr
- Mortgage credit (official guide) · Service-Public.gouv.fr