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Let's go through the exercises step by step. The exercises are mainly about converting different interest rates from one type to another (e.g., from nominal to effective rates), which involves the use of financial mathematics formulas.

### 1. Convertir una TNT de 3.01% capitalizable mensualmente en una TEA.
The formula to convert a **nominal interest rate (Tasa Nominal Total - TNT)** capitalized monthly to an **Annual Effective Rate (TEA)** is:

\[
TEA = \left(1 + \frac{TNT}{n}\right)^n - 1
\]

Where:
- $TNT = 3.01\%$,
- $n = 12$ (since the rate is capitalized monthly).

Substitute the values and compute the TEA.

---

### 2. Calcule la TES que originará una TNC de 2.75% con capitalización bimestral.
To convert a **Nominal Continuous Rate (Tasa Nominal Continua - TNC)** into an **Effective Semiannual Rate (TES)**, the relationship between them is given by:

\[
TES = e^{\frac{TNC}{n}} - 1
\]

Where:
- $TNC = 2.75\%$,
- $n = 6$ (since the rate is capitalized bimonthly, we convert it to a semiannual period).

---

### 3. Una persona depositó $15,000 con una TNM de 0.75% capitalizable bimestralmente. Calcule la TEA que originará el mismo interés que la TNM.
We use the same formula as in question 1, but in this case, the nominal monthly rate is converted to the TEA. The TNM (Tasa Nominal Mensual) is $0.75\%$, and we capitalize bimonthly. Thus, we convert it using the TEA formula.

---

### 4. Convertir una TEQ de 0.44% en una TET.
The conversion from **Quarterly Effective Rate (TEQ)** to **Triannual Effective Rate (TET)** involves using the formula:

\[
TET = (1 + TEQ)^3 - 1
\]

Where:
- $TEQ = 0.44\%$.

---

### 5. Convertir una TEA de 8.04% en una TEB.
To convert an **Annual Effective Rate (TEA)** to a **Biennial Effective Rate (TEB)**, use:

\[
TEB = (1 + TEA)^{\frac{1}{2}} - 1
\]

Where:
- $TEA = 8.04\%$.

---

### 6. Un préstamo de 20,000 devenga una TEB de 2.55%, si este préstamo se utilizó durante 125 días, ¿qué tasa efectiva debe aplicarse?
For this question, we need to calculate the **effective rate** for 125 days using the **biennial rate (TEB)**. The formula to find the **effective rate (TE)** for $ t $ days is:

\[
TE = \left(1 + TEB\right)^{\frac{t}{365}} - 1
\]

Where:
- $TEB = 2.55\%$,
- $t = 125$ days.

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Would you like me to solve any specific question from these steps in detail? Here are some related questions:

1. How does the capitalization period affect the effective interest rate?
2. What is the difference between a nominal rate and an effective rate?
3. How is the time factor in days incorporated into rate calculations?
4. What are the typical uses of TEA versus TEB in financial calculations?
5. How do continuous rates like TNC differ from periodic rates?

**Tip**: When comparing interest rates, always ensure they are expressed over the same time period (e.g., annual vs. annual) to make accurate comparisons.

Convertir una TNT de 3.01% capitalizable mensualmente en una TEA.
Calcule la TES que originará una TNC de 2.75% con capitalización bimestral.
Una persona depositó $15,000 con una TNM de 0.75% capitalizable bimestralmente. Calcule la TEA que originará el mismo interés que la TNM.
Convertir una TEQ de 0.44% en una TET.
Convertir una TEA de 8.04% en una TEB.
Un préstamo de 20,000 devenga una TEB de 2.55%, si este préstamo se utilizó durante 125 días, ¿qué tasa efectiva debe aplicarse?

Solve interest rate conversion problems including converting TNT to TEA, TNC to TES, and more. Understand financial concepts like compounding periods, nominal rates, and effective interest rates. Problems range from monthly to biennial rates.

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