Compound interest for a trader - the real one

Course 14: Personal Finance and Building Capital

Educational material only. It is not investment advice and it is not a promise of profit. All the calculations are mathematical illustrations. Past results do not guarantee future ones. Compound interest works both ways - losses compound too.

In financial marketing, compound interest is the “eighth wonder of the world” that turns 1,000 PLN into a million in 10 years at 50% a year. In real trading, compound interest is an accounting tool that works only when 4 conditions are met: positive expectancy, cost control, withdrawal control and drawdown control. Without those conditions, compounding means compounding losses and commissions.

This lesson debunks the myth and shows how to measure it correctly.

The goal of this lesson

After this lesson you will be able to:

1. calculate the real compound rate after costs, taxes and withdrawals.
2. Explain why withdrawing profit to live on breaks compounding and how to model it.
3. Understand the sequence of returns effect and why -20% hurts more than +20% pleases.
4. Build a simple capital projection sheet with three scenarios, without forecasting the market.

Why the marketing version does not work

A typical headline: “Earn 5% a month, after a year you have 79%”. It sounds good, but it leaves out:

• transaction costs (commissions, spreads)
• the 19% tax
• withdrawals to live on (MCU = monthly living costs)
• the drawdown that resets the base
• the fact that the rate is not constant every month, it has variance

The correct marketing formula:

final_capital = starting_capital * (1 + r)^n

The correct trader’s working formula:

real_final_capital = (((starting_capital * (1 + r_gross - cost_pct) - withdrawal) * (1 - effective_tax)) ^n with variance and drawdown

That no longer looks so spectacular.

Formula 1: Gross rate versus net rate

Assume your system generates an average of 2% a month gross (before costs). Commissions and spreads come to 0.4% a month. You pay tax once a year on net profit.

r_net_month = r_gross - monthly_costs
r_net_month = 2% - 0.4% = 1.6%

Annually gross: (1+0.02)^12 -1 = 26.8%
Annually net before tax: (1+0.016)^12 -1 = 21.0%
After 19% tax (simplification: on the whole annual profit): 21% * 0.81 = 17.0%

From a marketing 26.8% you drop to a real 17%. And that is without withdrawals and without variance.

If you add fixed costs (a platform at 1,200 PLN a year on 10k of capital = 12% a year), then:

r_real = 17% - 12% = 5% real

On 50k of capital the same 1,200 PLN cost is only 2.4%, r_real = 17% - 2.4% = 14.6%

The conclusion from Lesson 03 returns: small capital kills compounding with fixed costs.

Formula 2: The withdrawal effect - the compounding breaker

Most people building a small account withdraw the profits to live on. That breaks the snowball.

Model without withdrawals:

capital_n+1 = capital_n * (1 + r_net)

Model with a fixed withdrawal W covering part of the MCU:

capital_n+1 = (capital_n * (1 + r_net)) - W

Example:

• Capital 20,000 PLN
• r_net 1% a month
• A withdrawal of 500 PLN a month for the bills (because the emergency fund (WFA) has run out)

Month 1: 20,000 *1.01 = 20,200 -500 = 19,700 PLN. Capital shrinks despite a positive rate, because the withdrawal > the profit.

The KursTradera rule:

• As long as WFA < 12 and trading capital < 50k, you do not withdraw from the trading account to live on. Withdrawals are quarterly only, and only from the surplus > the base capital (see Lesson 04).
• A withdrawal breaks compounding. If you have to withdraw, this is not the compounding stage but the educational/testing stage, and do not count on a miracle.

Formula 3: Why -20% is not the same as +20% - asymmetry

Compound interest has a loss asymmetry.

Loss -10% -> you need +11.1% to get back to zero
Loss -20% -> you need +25% to get back
Loss -50% -> you need +100% to get back

The formula for the gain needed to recover:

required_gain = (1 / (1 - loss_pct)) -1

Example -30%: 1 / 0.7 = 1.428 -> +42.8%

That is why drawdown control matters more than chasing a high r.

For a trader this means: a system that earns +30% a year with a maxDD of -40% can be worse for compounding than a +15% system with a maxDD of -10%. The second has a smaller ruin potential and less stress, and stress leads to mistakes (Lesson 01).

Comparison table:

Systems B and C are easier to sustain behaviourally and to compound over the long term.

Formula 4: Projection with variance - 3 scenarios instead of 1 forecast

Never make a single projection of “I will make 25% a year for 10 years”. Make 3.

Assumptions:

• Starting capital: 10,000 PLN
• Monthly top-up from the trading pool: 600 PLN (in line with Lesson 04)
• Annual r_net scenarios: pessimistic 0%, base 5%, optimistic 12% (after costs and taxes)
• Horizon: 3 years = 36 months, contributions 600*36 = 21,600 PLN

A simplified formula with top-ups (without monthly compounding, for readability, annual steps):

capital_after_a_year = (starting_capital + sum_of_annual_topups) * (1 + r_annual)

Spreadsheet (logic):

// Pseudo-code for a spreadsheet:
cap = 10000
for year in 1..3:
  cap = cap + 12*600 // top-up
  cap = cap * (1 + r_scenario)

Results:

Even in the optimistic scenario of 12% a year net (which is very good), most of the growth comes from the top-ups (21,600 PLN), not from compounding magic. This is the real lesson: at the start, compounding builds the habit of topping up; only after years does it start building capital on its own.

That is why at KursTradera we first build the WFA and consistency, then we measure the edge, and only at the end do we calculate compounding.

When the plan says do not trade

When the plan says: DO NOT TRADE (compound interest context)

DO NOT LEAVE CAPITAL IN “BECAUSE IT WILL COMPOUND”, IF:

1. You do not know your r_net after costs and tax for the last 6 months. If you do not have that number, you have nothing to compound. It is fantasy.
2. You have an active max drawdown of >50% of the value from the last peak. Compounding losses is real. Stop, go back to your journal, describe your last 20 trades. Only then decide about further capital.
3. You withdrew >30% of the profit this quarter for impulse spending, despite WFA <6. You broke the breaker rule. Go back to the 3-account system.
4. You are projecting at r >20% a year net over the long term. That is a level only a few have historically sustained. Taking it into a financial plan is building a budget on a lottery win. Plan for 0-8% net and treat any surplus as a bonus.
5. You are topping up the account to “speed up compounding” at the expense of the emergency fund. That is inverting the pyramid. First WFA 6, then top-ups.

Compound interest likes boredom, time and not being touched. Trading likes activity. Reconcile the two with the portfolio separation from Lesson 04.

Mistakes that cost the most

1. Calculating compounding on gross capital, without deducting fixed costs. A platform at 100 PLN/month on 3,000 PLN of capital is -40% a year. No system recovers from that in a stable way. The result: frustration and leverage.

2. Ignoring tax in the projection. A 19% tax on profit is not a detail. With hundreds of trades a year, not setting aside a tax reserve ends in April with a loan to pay the Polish personal income tax (PIT).

3. Raising risk to “speed up” compounding. You raise risk from 1% to 3% per trade so that it grows faster. 3x the risk is 3x the drawdown. At 3% risk a -30% happens sooner and requires +42% to recover. It ends in your account being zeroed out.

4. Confusing the arithmetic and the geometric mean. The arithmetic mean of +10% and -10% is 0%. The geometric (compound) mean is: 100 1.10.9 = 99, that is -1%. In trading the geometric one is what counts. Two big losses destroy years of small gains.

geometric_mean = (product of (1+ri))^(1/n) -1

5. No reserve for the sequence. Even a good system can have 2 weaker years in a row at the start. If you start with 10k and have 2 years at 0%, while withdrawing to live on, you end up with 5k. Model 2 years at 0% as a standard scenario, not a catastrophic one.

Measurable exercise [35 minutes]

Name: 3-scenario calculator

1. 10 min - Input data: Open a spreadsheet. Enter:

• Trading capital START (e.g. 8,000 PLN)
• Monthly top-up to trading (e.g. 400 PLN) - only if WFA>=3
• Annual r_net from the last 6 months (if you do not have it, enter 0% as the base - more honest)
• Annual fixed costs (platform, data)

2. 10 min - Scenarios: Build 3 columns: Pessimistic r=0%, Base r=your_r_last_6m *0.5 (a discount!), Optimistic r=your_r_last_6m. Calculate the capital after 1, 2 and 3 years using the formula with top-ups and fixed costs.

3. 10 min - Withdrawal test: Add a “Quarterly withdrawal to live on” row = 0 PLN in the scenario without withdrawals and = MCU*0.2 in the scenario with withdrawals. See the difference after 3 years. Write down the conclusion.

4. 5 min - Decision: Write in your plan: “My capital grows mainly thanks to ___ (top-ups / profit). My r_real after costs is ___%. I will not project r > ___% into my budget.”

Completion measure: You have a spreadsheet with 3 final numbers and the awareness that on a small account top-ups account for 60-80% of the growth.

Check yourself

Question 1: Your system earned 20% gross this year. Commission and spread costs 6%, the platform 4% of capital, tax 19% on net profit. What is r_real? Answer: Profit after transaction costs: 20-6=14%. After fixed costs: 14-4=10%. After tax: 100.81=8.1% net real. Out of the marketing 20% you are left with a real 8.1%. That is still a good result, but it is not 20%.*

Question 2: Capital 10k, a -30% loss in a quarter. How much do you need to earn to get back, and why does it matter for compounding? Answer: You need +42.8%. At an r_real of 1% a month, that is 36 months of catching up. During that time you are not compounding forward, you are recovering. That is why loss control matters more than maximising profit - it protects the compounding curve.

Question 3: Why, at the start of building capital, are top-ups more important than the rate of return? Answer: Because the base is small. 10% of 10k is 1,000 PLN. A top-up of 7,000 PLN a year (600/month) is 7x more. Even doubling the rate from 10% to 20% gives only +1,000 PLN a year, while making the top-ups more consistent gives certain capital without raising risk. Compounding only starts to dominate at a larger base (50k+).

Frequently asked questions

Should I reinvest the whole profit? At the WFA<12 and capital <50k stage: yes, after setting aside a tax reserve. At the operating capital stage of 50k+: you can withdraw part of the profit under the rule from Lesson 04 (max 50% of net profit quarterly), and the rest stays to compound.

What annual rate is realistic long term after costs? There is no single number. As a working rule: plan for 0-8% net real as the base for your budget. Treat anything above that as a bonus, not a certainty. If your data from 200+ trades shows 12% net, use 6% for projections (a 50% discount for future degradation of the system and worse years).

Does compound interest work for a small 2,000 PLN account? Mathematically yes, in practice no. At 2,000 PLN fixed costs eat the effect. A small account is an educational project, where you measure R, profit factor and discipline, not compound interest. You switch compounding on when fixed costs are <5% of capital.

What should I do when I have 2 years in a row without profit? That is normal variance even in good systems. If your expectancy is positive (check your journal), you continue with the same risk. If you keep topping up consistently, capital grows despite no profit from the market (because of the top-ups). That is exactly what protects your budget - you are not dependent on the year.

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Summary: Compound interest for a trader is not a magic formula from an advert, it is bookkeeping: gross profit minus transaction costs minus fixed costs minus taxes minus withdrawals = what actually compounds. On top of that come the loss asymmetry and the sequence of returns. Build a 3-scenario spreadsheet, calculate r_real and accept that at the start 70% of the growth is your top-ups. Then compounding becomes an ally, and not a myth that leads to overleverage.

In the last lesson of the course: We will cover documenting your finances - how to keep a trader’s financial journal that combines budget, costs, taxes and results, so that in 10 minutes a week you know whether you are heading in the right direction.

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