Exercises: Module 01 — Introduction: Active vs. Passive Income¶

Instructions¶

Complete each exercise in order. Exercises increase in difficulty. Show your work — write out the calculations, not just the answer. Submit your answers by editing this file or committing a solutions file.

Easy Exercises (1–3)¶

Exercise 1¶

Difficulty: Easy Objective: Distinguish active from passive income

Classify each of the following income sources as Active (A) or Passive (P). If the classification depends on context, explain why.

1. Monthly salary from a CLT employment contract
2. Monthly dividends from 500 shares of ITUB4
3. Freelance web design project delivered last month
4. Monthly rent from a property you own
5. Interest earned on a CDB investment
6. Income from a YouTube channel you actively manage
7. Royalties from a book you wrote three years ago
8. Money earned teaching an online class live each week

Your answers:

Exercise 2¶

Difficulty: Easy Objective: Calculate a basic emergency fund target

Helena earns R$ 4.200/mês and has the following monthly expenses:

1. What is Helena's total monthly expense?
2. What is Helena's minimum emergency fund (3 months)?
3. What is her conservative emergency fund (6 months)?
4. Helena works as MEI (autonomous). Should she use 3 months or 6 months as her target? Why?
5. She currently has R$ 1.500 saved. How many months will it take to reach the 6-month target if she saves R$ 500/mês?

Your answers:

Exercise 3¶

Difficulty: Easy Objective: Apply the investment pyramid

Rodrigo has just reached his 3-month emergency fund target. He now has an additional R$ 500/mês to invest. Using the investment pyramid, sort the following options into the correct level (1, 2, or 3) and explain which Rodrigo should prioritize next:

• Buying PETR4 ações (individual stock, high volatility)
• Additional top-up to emergency fund (reaching 6-month target)
• Tesouro IPCA+ with 3-year maturity
• A speculative cryptocurrency with no established track record
• LCI from a digital bank paying 11% CDI exempt, 1-year maturity

Your answers:

Medium Exercises (4–6)¶

Exercise 4¶

Difficulty: Medium Objective: Compare net yields across renda fixa instruments

Calculate the net yield for each of the following investments for an investor with a 12-month horizon (i.e., money invested for 361–720 days, IR = 17.5% for this bracket):

1. Complete the Net Yield column
2. Rank the instruments from best to worst net yield for a 12-month horizon
3. Does your ranking change for a 2-year horizon (IR = 15%)? Recalculate and explain.

Your answers:

Exercise 5¶

Difficulty: Medium Objective: Compound interest calculation

Use the formula M = PMT × [((1+i)^n - 1) / i] where needed.

1. Marcelo invests R$ 300/mês at 0.8%/mês for 10 years. What is his final balance?
2. Carla invests R$ 300/mês at 0.8%/mês for 20 years. What is her final balance?
3. How much more does Carla have compared to Marcelo despite only contributing for twice as long?
4. Marcelo decides to invest R$ 600/mês instead of R$ 300/mês for the same 10 years. Does doubling his contribution double his final balance? Why or why not?
5. What monthly contribution rate would Marcelo need to invest to match Carla's final balance in only 10 years?

Your answers:

Exercise 6¶

Difficulty: Medium Objective: Understand inflation's impact on real returns

SELIC is at 10.5% per year. IPCA (inflation) is at 5.1% per year.

1. Calculate the real return on Tesouro Selic using the correct formula: real = ((1 + nominal) / (1 + inflation)) - 1
2. A poupança account yields 70% of SELIC (since SELIC > 8.5%). Calculate the poupança real return.
3. Joana has R$ 50.000 in poupança and R$ 50.000 in Tesouro Selic. After 5 years, how much more (in real terms) does the Tesouro Selic hold have?
4. If Joana had started at age 30 and is now 55 (25 years later), what was the total real purchasing power lost by choosing poupança over Tesouro Selic?

Your answers:

Hard Exercises (7–8)¶

Exercise 7¶

Difficulty: Hard Objective: Analyze a complete financial situation and prescribe the correct next steps

Pedro, age 32, has the following financial profile: - CLT salary: R$ 7.000/mês gross (R$ 5.400 net after INSS/IR) - Monthly expenses: R$ 4.200 - Current savings: R$ 3.000 in a CDB liquidez diária (102% CDI) - Credit card debt: R$ 4.500 at 18%/mês (yes, per month — this is common in Brazil) - No other investments

1. Should Pedro first pay off the credit card debt or build the emergency fund? Show the math that justifies your answer.
2. Assuming he eliminates the credit card debt first, how many months does that take at his current savings rate?
3. After eliminating the debt, what is his new monthly investable surplus?
4. Write a 3-step action plan for Pedro over the next 24 months (what to do in each phase) using the investment pyramid framework.
5. What is Pedro's financial position (approximate portfolio value) at the end of month 24, assuming all goes according to plan?

Your answers:

Exercise 8¶

Difficulty: Hard Objective: Build a financial independence calculation

Luciana, age 27, lives in São Paulo with monthly expenses of R$ 5.000/mês. She wants to achieve financial independence by age 50 — 23 years from now. She plans to live on her investment income with no salary.

1. Using the 4% Safe Withdrawal Rate (SWR), how much total patrimônio does Luciana need?
2. Accounting for 5% annual inflation, what will R$ 5.000/mês of today's expenses be in nominal terms at age 50?
3. Recalculate the required patrimônio at age 50 using the inflation-adjusted expense figure.
4. If Luciana invests R$ 2.000/mês starting today at an average return of 0.9%/mês (approximately 11.4% per year), will she reach her target by age 50?
5. If not, what monthly contribution would she need?

Show all calculations.

Your answers:

Expert Exercise (9)¶

Exercise 9¶

Difficulty: Expert Objective: Synthesize all module concepts into a complete personal financial assessment

This exercise requires you to apply this module to your own life. Be honest — there is no "right answer" here, only rigor.

1. Income audit: List all your current income sources. Classify each as active or passive. Calculate what percentage of your total income is passive today.

2. Emergency fund audit: Calculate your exact monthly expenses (use your actual bank/credit card data for the last 3 months). Calculate your emergency fund target. Calculate how much you currently have vs. the target. Calculate the gap.

3. Poupança audit: If you have any money in poupança, calculate how much real purchasing power you have lost in the last 2 years compared to keeping it in Tesouro Selic. (Use 2022–2024 average SELIC of approximately 12.5% and poupança of approximately 8.75% for this period.)

4. 10-year projection: Pick a target passive income level (the amount you would need/month to cover your expenses). Calculate the patrimônio needed. Calculate how many years it would take to reach that patrimônio investing your current monthly savings surplus at 0.8%/mês.

5. One action: Based on the above, identify the single highest-leverage action you can take this week to improve your financial situation. Write it as a concrete, specific task with a deadline.

Your answers:

Answer Key¶

See ANSWERS.md for the answer key after attempting all exercises.