¿A qué tasa mensual de interés se colocó un capital de $20.000, si luego de 27 meses, se transformó en un monto de $38.956?

Para determinar la tasa mensual de interés, podemos usar la fórmula del **interés compuesto**, que es la siguiente:

\[
M = C \times (1 + i)^n
\]

Donde:
- $ M $ es el monto final ($38.956),
- $ C $ es el capital inicial ($20.000),
- $ i $ es la tasa mensual de interés (lo que queremos encontrar),
- $ n $ es el número de periodos (27 meses).

Reorganizando la fórmula para despejar $ i $, obtenemos:

\[
i = \left( \frac{M}{C} \right)^{\frac{1}{n}} - 1
\]

Sustituyendo los valores:

\[
i = \left( \frac{38.956}{20.000} \right)^{\frac{1}{27}} - 1
\]

Voy a calcular el valor exacto para determinar la tasa de interés mensual.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can manually calculate the rate by following these steps:

1. Divide the final amount ($38.956) by the initial capital ($20.000):  
   \[
   \frac{38.956}{20.000} = 1.9478
   \]
   
2. Take the 27th root of this result:  
   \[
   \left( 1.9478 \right)^{\frac{1}{27}} = 1.0243
   \]
   
3. Subtract 1 from the result to get the interest rate:  
   \[
   1.0243 - 1 = 0.0243
   \]

So, the monthly interest rate is approximately **2.43%**.

Would you like more details or further clarification?

Here are 5 related questions you might find interesting:
1. How is compound interest different from simple interest?
2. What is the formula for calculating the number of periods in compound interest?
3. How do nominal and effective interest rates differ?
4. What factors influence interest rates in an economy?
5. How can one calculate continuous compound interest?

**Tip:** When calculating interest rates, always ensure that the period of time matches the rate (monthly rate for months, annual rate for years).

Descubre cómo calcular la tasa mensual de interés utilizando la fórmula del interés compuesto. Dado un capital inicial de $20.000 y un monto final de $38.956 después de 27 meses, este problema detalla paso a paso cómo determinar una tasa mensual de interés del 2.43%.

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