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II.- Un estudiante de posgrado planea realizar su doctorado en el extranjer de un dinero que le proporcionauna renta de \( \$ 500.00 \) pesos y que es dep años en una cuenta bancaria que le premia con \( 9 \% \) anual. convertible men

Ask by Little Paul. in Mexico
Mar 18,2025

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El estudiante deposita \$500 mensuales en una cuenta con un interés anual del 9%, convertible mensualmente. Al cabo de \( t \) años, el monto acumulado será: \[ S = 500 \cdot \frac{(1.0075)^{12t} - 1}{0.0075} \] Donde: - \( t \) = número de años - \( 1.0075 \) = 1 + tasa mensual (\( 0.09/12 = 0.0075 \)) - \( 12t \) = número total de depósitos mensuales Este cálculo da la cantidad total en la cuenta después de \( t \) años.

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Beyond the Answer

¡Claro! Imagina que este estudiante quiere conocer cuánto dinero tendrá en su cuenta al final de su doctorado. Si depositas \( \$ 500.00 \) pesos anuales en una cuenta que ofrece un interés del \( 9\% \) convertible mensualmente, puedes usar la fórmula del valor futuro de una serie de pagos. Con un poco de cálculo, puedes descubrir que al final de esos años, su suma puede crecer exponencialmente gracias a la magia del interés compuesto. A la hora de ahorrar, asegúrate de hacer un seguimiento de tus depósitos y los intereses que acumulas. Un error común es no considerar que los intereses se capitalizan, es decir, que también se generan intereses sobre los intereses. Si no llevas un registro, podrías subestimar tus ahorros. Un buen consejo es usar una hoja de cálculo para visualizar cómo ese dinero crece con el tiempo, ¡te sorprenderás de lo que puedes acumular!

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