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The problem discusses a person in Colombia with investments in U.S. dollars and the assumption that the exchange rate remains constant at 1 USD = 2,000 Colombian pesos. The investment in U.S. dollars yields a 3% return, and the person’s friend claims that the same 3% gain will be seen in Colombian pesos.

Let’s analyze the given options to determine the correctness of the friend's statement:

- **Option A**: 
  - Claims that the friend's statement is correct, and it suggests that, regardless of exchange rate fluctuations, the proportion of increase in both currencies is the same. This is incorrect because the return should be considered based on the exchange rate stability, but it does not imply an automatic equivalence in the rate of return between currencies unless specified clearly.

- **Option B**: 
  - States that the friend's claim is incorrect because knowing the exact investment value is necessary to calculate the amount of gain. This argument focuses on the practical side of calculating returns but doesn't fully address the proportionality of the 3% in different currencies.

- **Option C**: 
  - This option claims that the friend's statement is correct because the 3% represents a fixed proportion in either currency, given that the exchange rate stays constant. This is the most accurate reasoning. Since the exchange rate is fixed, the 3% gain in U.S. dollars will indeed translate to a 3% gain in Colombian pesos.

- **Option D**: 
  - Claims the statement is incorrect because the 3% increase would be larger in pesos, as each dollar equals 2,000 pesos. This is incorrect because, while each dollar is worth 2,000 pesos, the percentage gain would still be the same in both currencies, given the fixed exchange rate.

### Conclusion:
The correct answer is **C** because if the exchange rate remains constant, the 3% increase in U.S. dollars will translate directly to a 3% increase in Colombian pesos.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does a constant exchange rate affect investment returns when converting between two currencies?
2. What would happen to the returns in pesos if the exchange rate fluctuates instead of staying constant?
3. Can we always expect the same percentage gain in different currencies with a fixed exchange rate?
4. What would be the impact on returns if the investment had a higher interest rate in dollars?
5. How can inflation affect the real returns of this investment in either currency?

**Tip**: Always consider exchange rate fluctuations when dealing with foreign investments, as they can impact your actual returns when converting between currencies.

Una persona que vive en Colombia tiene inversiones en dólares en Estados Unidos, y sabe que la tasa de cambio del dólar respecto al peso colombiano se mantendrá constante este mes, siendo 1 dólar equivalente a 2,000 pesos colombianos y que su inversión, en dólares, le dará ganancias del 3 % en el mismo periodo. Un amigo le asegura que en pesos sus ganancias también serán del 3 %. ¿La afirmación de su amigo es correcta?

Esta pregunta examina la relación entre la tasa de cambio y el rendimiento de inversiones en dólares cuando la tasa de cambio entre dólares y pesos colombianos se mantiene constante. Analiza cómo el 3% de ganancia en dólares afecta la ganancia en pesos colombianos. Apto para estudiantes de niveles superiores (Grados 10-12).

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