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TAE – TIN Calculator (Spain)

Convert TIN to TAE and back: what rate you really pay or earn over a year when the nominal rate compounds monthly, quarterly or daily, with the Banco de España formula explained.

The TAE a bank publishes for a loan or deposit may also include fees and costs; this conversion is the purely financial part of the interest rate.

Equivalent TAE
5.1162 %

Formula: TAE = (1 + TIN/k)^k − 1, with k compounding periods per year.

Educational tool based on the financial equivalence of rates (Banco de España, Circular 5/2012). A product's regulated TAE may include fees: always compare the official TAE of the offer.

1

TIN and TAE: two numbers for the same product

The TIN (nominal interest rate) is the "label" annual rate: the one used to compute each instalment or interest credit. The TAE (effective annual rate) is what that rate really amounts to over a year when interest compounds several times: each settlement earns interest on the previous ones. That is why a 5% TIN compounded monthly equals a 5.116% TAE.

2

The formula, and why frequency matters

TAE = (1 + TIN/k)^k − 1, where k is the number of compounding periods per year: 12 for monthly, 4 quarterly, 365 daily. The larger k is, the further the TAE moves from the TIN: compound interest working within the year. With annual compounding (k = 1), TIN and TAE coincide.

3

The advertised TAE includes something more

For loans and consumer credit, the TAE a bank must publish also folds in fees and mandatory costs (Banco de España Circular 5/2012). This calculator does the pure financial part (rate and compounding), which has a name of its own: the Banco de España calls it the TEDR, the interest-rate component of the TAE without fees. The official TAE of an offer with fees will be higher than the TEDR you get here. To compare offers, always use each one's official TAE.

4

For deposits it works the same way, in your favour

On a deposit or interest-bearing account the logic is identical but you are the one collecting: a 3% TIN with monthly interest credits yields a 3.042% TAE if you reinvest them. The difference looks small; on large amounts and horizons it stops being small. The compound interest calculator shows by how much.

Worked example

Example: a mortgage advertises a 5% TIN with monthly instalments. TAE = (1 + 0.05/12)¹² − 1 = 5.1162%. In reverse: if a deposit promises a 5% TAE with monthly credits, the TIN behind it is 12 × (1.05^(1/12) − 1) = 4.8889%.

Frequently asked questions

What is the difference between TIN and TAE?
The TIN is the nominal annual rate instalments are computed with; the TAE expresses the effective annual cost or yield accounting for how often interest compounds and, in the regulated TAE of loans, fees as well.
Why is the TAE higher than the TIN?
Because with compounding more frequent than annual, each period's interest earns interest in the following periods within the same year. Only with annual compounding do the two coincide.
Can the TAE be lower than the TIN?
In the pure financial conversion, no: at most equal (annual compounding). In real products, a TAE below the TIN usually signals bonuses or promotional arithmetic worth reading closely.
Is this TAE the same as the one in loan adverts?
Not exactly: a loan's regulated TAE also includes fees and mandatory costs. This conversion is the mathematical equivalence between rates; only the lender can state an offer's official TAE.
Which compounding frequency should I pick?
The product's: monthly for most mortgages, loans and monthly-credit deposits; quarterly or half-yearly for some deposits; daily for certain interest-bearing accounts. It appears in the contract or the pre-contractual information.

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Author: Thorben Rasmus Idel · Reviewed by: Nahar Geva · Last reviewed: