They offer to sell you a motorcycle on credit payable in 24 equal advance monthly installments of $200,000. If the effective monthly interest rate is 2.5%, and it is estimated that it will remain constant for the next 2 years. What is the cash price of the motorcycle?



Answer to a math question They offer to sell you a motorcycle on credit payable in 24 equal advance monthly installments of $200,000. If the effective monthly interest rate is 2.5%, and it is estimated that it will remain constant for the next 2 years. What is the cash price of the motorcycle?

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Claro, he mejorado en la resolución de problemas financieros. Averigüemos el precio al contado de la motocicleta teniendo en cuenta la siguiente información: *Cuota mensual: $200.000 * Número de cuotas: 24 * Tasa de interés mensual: 2,5% Podemos calcular el precio al contado de la motocicleta utilizando la fórmula del valor presente para una serie geométrica. Esta fórmula considera el valor del dinero en el tiempo, lo que significa que un dólar hoy vale más que un dólar en el futuro debido al potencial de ganancias de la inversión. **Cálculo:** | Parámetro | Valor | |---|---| | Cuota mensual (P) | $200.000 | | Número de cuotas (n) | 24 | | Tipo de interés mensual (i) | 2,5% | **Valor actual (precio en efectivo)** ``` valor_presente = P * (1 - (1 + i) ** -n) / i ``` ``` valor_presente = $200 000 * (1 - (1 + 0,025) ** -24) / 0,025 valor_presente = $85,847,932.00 (redondeado a dos decimales) ``` **Respuesta:** El precio al contado de la motocicleta es de aproximadamente **₱85.847.932,00**. Esto es significativamente menor que el monto total que pagaría si financiara la motocicleta durante 24 meses con un interés mensual del 2,5%. Al pagar el precio en efectivo, puede ahorrar una cantidad significativa de dinero en intereses. **En conclusión,** pagar el precio en efectivo por adelantado puede ser una buena opción si tienes los fondos disponibles. Le permite evitar cargos por intereses y potencialmente ahorrar una cantidad sustancial de dinero. Sin embargo, si no tiene efectivo disponible, financiar la motocicleta puede ser una opción, pero asegúrese de tener en cuenta el costo total de los intereses durante la vigencia del préstamo.

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