Se depositan $56.800 en un plazo fijo y se retiran $67.980 a los siete meses. Si la capitalización es mensual, la TEA y la TNA de la operación son:

Para resolver este problema, necesitamos encontrar la Tasa Efectiva Anual (TEA) y la Tasa Nominal Anual (TNA) del depósito a plazo fijo. A continuación, desglosamos los cálculos:

### 1. Datos Iniciales
- **Monto Inicial (C):** \$56,800
- **Monto Final (M):** \$67,980
- **Tiempo (n):** 7 meses
- **Capitalización:** Mensual

### 2. Fórmula para la Tasa Efectiva Mensual (TEM)
Dado que la capitalización es mensual, podemos usar la fórmula del interés compuesto:
\[
M = C \times (1 + r)^n
\]
Donde:
- $ M $ es el monto final
- $ C $ es el capital inicial
- $ r $ es la tasa efectiva mensual (TEM)
- $ n $ es el número de periodos (7 meses en este caso)

Sustituyendo los valores dados:
\[
67,980 = 56,800 \times (1 + r)^7
\]

### 3. Despejar la Tasa Efectiva Mensual (TEM)
Para encontrar $ r $:
\[
\frac{67,980}{56,800} = (1 + r)^7
\]
\[
1.196478873 = (1 + r)^7
\]

Ahora tomamos la raíz séptima para despejar $ r $:
\[
(1 + r) = \sqrt[7]{1.196478873}
\]

\[
r = \sqrt[7]{1.196478873} - 1
\]

### 4. Cálculo de $ r $ y Conversión a Porcentaje
Ahora realizamos los cálculos necesarios.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can still guide you through the process manually if you'd like to continue the calculation step-by-step with a calculator. Here's a recap of where we left off:

1. We have the equation $ r = \sqrt[7]{1.196478873} - 1 $.
2. The next step is to calculate this value using a calculator to find the monthly interest rate.
3. After finding the monthly rate, we can proceed to find the TEA and TNA.

Would you like to proceed with a step-by-step explanation using a calculator, or do you have any questions about the process so far?

Here are 5 related questions that might help you further:
1. How do you calculate the TEA once you have the monthly rate?
2. What is the difference between the TEA and the TNA?
3. How would the calculation change if the capital was compounded quarterly instead of monthly?
4. Can the formula $ M = C \times (1 + r)^n $ be used for other periods like days or years?
5. How does the compounding frequency affect the final amount in an investment?

**Tip:** When calculating interest rates, be mindful of the compounding period (monthly, quarterly, yearly) as it significantly impacts the final amount.

Learn how to calculate the Tasa Efectiva Anual (TEA) and Tasa Nominal Anual (TNA) for a fixed deposit where $56,800 grows to $67,980 in 7 months with monthly compounding. This step-by-step guide uses compound interest formulas to solve for the effective monthly interest rate, TEA, and TNA. Suitable for Grades 10-12.

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