
## Compound Interest vs CAGR - Not the Same (But We Use Them Interchangeably)

There's a phrase repeated ad nauseam in the investing world: "Compound interest is the eighth wonder of the world" (supposedly said by Einstein, though probably not). The problem is that when we talk about stock market investing, **technically we're not talking about compound interest**. We're talking about CAGR.

So why does everyone keep using the term "compound interest" anyway? Because it's become the standard. It's incorrect, yes, but it is what it is. Let's unravel this little white lie of the financial world.

### What is compound interest really?

Compound interest is a mathematical concept applied to **fixed-rate debt instruments**. Think of:

- A savings account that gives you a guaranteed 2% annually
- A bond that pays a fixed 3% coupon annually
- A fixed-term deposit with a known interest rate

The magic of compound interest is simple: **you earn interest on your interest**. If you have $1000 at 5% annually:

- Year 1: $1000 × 1.05 = $1050
- Year 2: $1050 × 1.05 = $1102.50 (not $1100)
- Year 3: $1102.50 × 1.05 = $1157.63

The formula is straightforward:

**Final Value = Initial Capital × (1 + interest)^years**

The important thing here is that the **interest is known, fixed, and predictable**. You know exactly how much you'll have in 10 years.

### So what is CAGR then?

CAGR stands for **Compound Annual Growth Rate**. It's a measure used to calculate **the average annual return of an investment** whose value fluctuates.

The key difference: **CAGR is calculated backwards, looking at the past**. It doesn't predict the future, it simplifies the past.

Imagine you invest $1000 in stocks:

- Year 1: +20% → $1200
- Year 2: -10% → $1080
- Year 3: +15% → $1242

What was your average annual return? This is where CAGR comes in:

**CAGR = (Final Value / Initial Value)^(1/years) - 1**

**CAGR = (1242 / 1000)^(1/3) - 1 = 7.49% annually**

CAGR tells you: "If you had grown at a constant rate each year instead of having those ups and downs, you would have grown at 7.49% annually." It's a **useful simplification**, but it doesn't reflect the reality of what happened.

### The fundamental difference

Here's the crux:

| Concept | Compound Interest | CAGR |
|:---------|:-----------------|:-----|
| **Application** | Fixed-rate debt instruments | Investments with variable returns |
| **Direction** | Calculated forward (predictive) | Calculated backward (descriptive) |
| **Certainty** | You know the result in advance | You describe what already happened |
| **Volatility** | Doesn't exist, growth is linear | Simplifies actual volatility |
| **Example** | 2% annual deposit | Stock investment that went from $1000 to $1500 |

### Why do we misuse the term?

Because **it sounds good**. "Compound interest" has that air of mathematical magic that attracts. Plus, the formula looks the same on the surface:

- Compound interest: `1000 × (1.05)^10`
- Projected CAGR: `1000 × (1.08)^10`

Visually they're identical, but conceptually they're different worlds. In the first case, that 5% is **guaranteed**. In the second, that 8% is a **hope** based on historical data.

### The problem with applying compound interest to stocks

When someone says "If you invest $10,000 at 8% annually for 30 years you'll have $100,626," they're using the compound interest formula for something that **doesn't have a fixed interest rate**.

The stock market doesn't guarantee you 8% annually. It might give you +30% one year and -20% the next. The end result might be similar, but the journey is completely different. And that journey matters because:

1. **It affects your psychology**: Seeing your investment drop 40% hurts, even if it recovers "in the long run"
2. **Timing matters**: If you need the money in a bad year, you're screwed
3. **Volatility has a cost**: It's not the same to grow at a constant 8% as to go up 50% and down 30%

### So what term should we use?

Technically, when talking about stock market investing we should say:

- **"Annualized compound return"** (more precise)
- **"Historical CAGR"** (if talking about the past)
- **"Expected return"** (if projecting into the future)

But let's be realistic, everyone says "compound interest" and everyone understands what we're talking about.

### Conclusion: use the term, but understand the difference

Will I continue using "compound interest" when talking about stock market investing? Probably yes. Is it wrong? Technically yes. Does it matter?

**Yes, it matters to understand the difference**. Not because you need to correct everyone on the Internet (please don't), but because **it changes how you invest**:

- Compound interest is predictable → plan with certainty
- CAGR is descriptive → plan with uncertainty

When you project your retirement assuming a 7% annual "compound" return, you're not making an exact mathematical projection. You're making an **estimate** based on historical averages that may or may not hold true.

And that's fine, as long as you're aware of it.

So yes, keep using the term "compound interest" in your investment discussions. But keep in mind that you're simplifying. Reality is more volatile, more uncertain, and honestly, more interesting.

In the end, what matters isn't using the 100% correct term, but **understanding what's behind** that compound growth. And now, if someone corrects you at a family dinner because you said "compound interest" instead of "CAGR," you know what to say: "Technically you're right, but socially you're being annoying" 😄


Compound Interest vs CAGR - Not the Same (But We Use Them Interchangeably)


## Solidarity Fee 2025 - How Does It Affect My Salary?

In 2025, the government has introduced a solidarity fee for "high incomes" - those exceeding the maximum contribution base, which has increased to **€58,914** in 2025. If you don't want to read the details, go straight to the calculator where I've already included this new fee: [**Net Salary Calculator**](/en/spanish-net-salary-calculator!new).

### How is it calculated?

It's a tax that, similar to MEI, will increase progressively 🫠

The solidarity fee doesn't affect you if your gross salary is below the maximum solidarity quota of €58,914.

Otherwise, the following brackets apply:

| From      | To               | Total Rate | Employee | Employer |
| :-------- | :--------------- | ---------: | -------: | -------: |
| €58,914   | €64,805.4 (110%) |      0.92% |    0.15% |    0.77% |
| €64,805.4 | €88,371 (150%)   |         1% |    0.17% |    0.83% |
| €88,371   | ...              |      1.17% |    0.19% |    0.98% |

**Important**: The distribution between employer and employee maintains the same proportion as common contingencies contributions (83.39% employer and 16.61% employee).

From the maximum social security quota (€58,914) to "maximum quota + 10%" (€64,805.4), 0.92% total applies (0.15% employee + 0.77% employer).
From €64,805.4 to "maximum quota + 50%" (€88,371), 1% total applies (0.17% employee + 0.83% employer).
Finally, from €88,371 onwards, 1.17% total applies (0.19% employee + 0.98% employer).

### Example

Let's look at an example with a salary of €100,000 in Catalonia. Let's compare 2024 and 2025.

![Monthly salary of 100k in Catalonia at 2024 compared to 2025](/images/100k-catalunya-2024-2025.jpeg)

As we can verify, it drops from €5,320.61 to €5,310.55. Approximately €10 less net per month.

![Solidarity fee for 100k monthly salary in 2025 Catalonia](/images/100k-catalunya-2025-cuota-solidaridad.png)

### Future

Finally, let's see the planned evolution of this tax until 2045.

| Year | Rate up to additional 10% | Bracket between additional 10%-50% | Brackets additional >50% |
| ---: | ------------------------: | ---------------------------------: | -----------------------: |
| 2025 |                     0.92% |                              1.00% |                    1.17% |
| 2026 |                     1.15% |                              1.25% |                    1.46% |
| 2027 |                     1.38% |                              1.50% |                    1.75% |
| 2028 |                     1.60% |                              1.75% |                    2.04% |
| 2029 |                     1.83% |                              2.00% |                    2.33% |
| 2030 |                     2.06% |                              2.25% |                    2.63% |
| 2031 |                     2.29% |                              2.50% |                    2.92% |
| 2032 |                     2.52% |                              2.75% |                    3.21% |
| 2033 |                     2.75% |                              3.00% |                    3.50% |
| 2034 |                     2.98% |                              3.25% |                    3.79% |
| 2035 |                     3.21% |                              3.50% |                    4.08% |
| 2036 |                     3.44% |                              3.75% |                    4.38% |
| 2037 |                     3.67% |                              4.00% |                    4.67% |
| 2038 |                     3.90% |                              4.25% |                    4.96% |
| 2039 |                     4.13% |                              4.50% |                    5.25% |
| 2040 |                     4.35% |                              4.75% |                    5.54% |
| 2041 |                     4.58% |                              5.00% |                    5.83% |
| 2042 |                     4.81% |                              5.25% |                    6.13% |
| 2043 |                     5.04% |                              5.50% |                    6.42% |
| 2044 |                     5.27% |                              5.75% |                    6.71% |
| 2045 |                     5.50% |                              6.00% |                    7.00% |


Solidarity Fee 2025 - How Does It Affect My Salary?


## How is net salary calculated

Imagine you have a job offer, a tempting new annual gross salary, but what's the monthly net amount? What's the exact salary increase? Imagine being able to compare your current salary with your future one simply by dragging a slider. I bring you the solution:

💰 [**Net Salary Calculator**](/en/spanish-net-salary-calculator!new)

If you're like me, to calculate net salary from gross, you'd resort to the [first Google result](https://cincodias.elpais.com/herramientas/calculadora-sueldo-neto/!new). Constantly scrolling up and down, refreshing the page which, by the way, is barely usable on mobile.

And if you wanted to be precise, you'd create an Excel with the typical tax bracket table and calculate it manually:

![State IRPF Brackets](/images/tramos.jpg)

That's it, right? Well, no... to properly calculate the real net salary, there are many more details to consider.

One day I wanted to slay this dragon and understand as best as possible how it's calculated. While researching, I developed this [net salary calculator](/en/spanish-net-salary-calculator!new) to validate what I was learning.

### Basic knowledge first 🧑‍🏫

There's a kind of urban legend that says: _"If they raise your salary and you change tax brackets, you might end up earning less."_ I've heard it several times and it perfectly explains how little financial education there is in schools. I guess learning that someone parted the seas and multiplied bread is more important... well, I'm getting off track.

NO.

**It's impossible for a salary increase to result in earning less net income**. The brackets are cumulative. Example, let's imagine that Paco earns €30,000 gross per year:

The first €12,450 has 19% withholding.
What's between €12,450 and €20,200, that is, the next €7,750 has 24% withholding.
Finally, the difference between €26,059 and €20,200 => €5,895 has 30% withholding.

The first part of the salary will always have a lower withholding and increases progressively in each bracket. I've tried to show this through graphs in the [calculator](/en/spanish-net-salary-calculator!new), try it out.

![Explained Brackets](/images/tramosExplicados.png)

### Expenses 🚗

If you've been reading carefully, you'll have noticed that in the last subtraction I didn't use €30,000 but €26,059. One of the reasons is expenses.

There's a minimum expense of €2,000, all calculations must be made by initially subtracting this value from the gross, in Paco's case, after subtracting expenses we're left with €28,000. But this figure still isn't €26,059, what's missing? Social Security.

### Social Security 🏥

Besides expenses, another concept to deduct before calculating IRPF is Social Security. This should be easy, it's 6.47% but with a nuance, [there's a minimum and maximum](https://www.campmanyabogados.com/blog/bases-cotizacion!new). The maximum is reached at €56,646 gross annually, all salaries above that pay the same. The minimum\* is €15,120 gross annually. All this data applies to 2024. They've been increasing each year.

Paco has a Social Security payment of €1,941 which if we subtract from €28,000 we already have the figure I used in the previous calculation. Let's name everything.

### Taxable Base

`Taxable Base = Gross Salary - Expenses - Social Security`
`€26,059 = €30,000 - €2,000 - €1,941`

### State and Regional IRPF

Now yes, with the taxable base we can calculate the IRPF.

Online calculators usually only show you some IRPF brackets. Those brackets are the state ones and apply to everyone except Basques and Navarrese. What we don't usually take into account is that each autonomous community has its brackets, and they're ALL different. [Check the breakdown of IRPF brackets for each autonomous community in Spain in the corresponding tab](/en/spanish-net-salary-calculator!new).

![IRPF brackets for each community](/images/tramos-comunidades.png)

The typical State table only applies to non-resident Spaniards, if you reside in Spanish territory, your community's table and the state table are used (**with half the percentage in each bracket**). Notice in the image how the state percentages are now 9.5%, 12% and 15% instead of 19%, 24% and 30%.

![State and Catalan IRPF brackets](/images/IRPF-estatal-y-autonomico.png)

I've added the option to see the aggregated brackets, to make it visually easier to see the different brackets that apply to you.

![Aggregated State and Catalan IRPF brackets](/images/IRPF-estatal-y-autonomico-agregados.png)

We could calculate the IRPF but first, let's talk about deductions.

### Deductions

You might be familiar with the figure €5,550. It's the deductible minimum. In the most common case, single person without children etc., they have that deductible minimum. To deduct it, brackets are also applied. That is, to know how much we can deduct if we live in Catalonia we have to apply both the state and autonomous community brackets to the figure to be deducted. Example:

€5,550 is in both the first State bracket (up to €12,450) and Catalonia's (up to €12,450), therefore the first bracket rate applies:

- State 9.5% - €527.25
- Catalonia 10.5% - €582.75

The total state taxes are reduced by the calculated deduction, same with the autonomous community.

`IRPF = IRPF taxable base (brackets) - deductions (brackets)`

This is the standard case, deductions increase for each child, for each dependent ancestor, etc. I've included most of these cases in the [net salary calculator](/en/spanish-net-salary-calculator!new).

Let's imagine Paco has twins, 2 children under 3 years old. Well, the deductions increase to:

- State 4.66% - €1,035.5
- Catalonia 5.2% - €1,144.5

The resulting monthly net salary with 12 payments is €2,007.45, which compared to the salary without children (€1,918.29) results in €89.16 more per month for having two children under 3 years old, not sure if it's enough for diapers 😄.

I've added this data in the calculator

![Deduction Benefit](/images/beneficio-deduccion.png)

_Keep in mind that I'm assuming Paco makes an individual tax declaration, therefore the deduction is 50%. If he files jointly (only married couples), he gets 100%, double the deduction than individual._

### The Formula 🎉

The final formula for calculating your net salary is as follows:

`Net Salary = Gross Salary - Expenses - Social Security - State IRPF - Regional IRPF`

With the nuances already mentioned:

- IRPF and its deductions are calculated on the taxable base and with the corresponding brackets.
- There's a minimum and maximum for Social Security.

I hope to have clarified a bit how this calculation works, it's important to know this information.

Details like MEI, flexible compensation, Beckham Law, etc. are missing. I'll explain them in future entries.

##### Sources

- [IRPF tables by autonomous communities](https://www.businessinsider.es/tablas-irpf-comunidades-autonomas-cuanto-pagas-renta-625415)
- [How the IRPF percentage is calculated](https://ekuatio.com/como-se-calcula-el-porcentaje-de-irpf-en-la-nomina/)
- [Withholding calculation](https://www2.agenciatributaria.gob.es/wlpl/PRET-R170/index.zul)
- [How much you can deduct on your taxes for your children](https://www.finect.com/usuario/Josetrecet/articulos/hijos-declaracion-renta)


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