Question
2. A home appliance store sells washing machines with the following conditions: S/. 2,000 as the first payment and 11 additional monthly payments that decrease by 5% each month with respect to the previous payment. If the effective interest is 15% per year, what is the amount to be paid in cash for the purchase of the washing machine? And what is the amount of interest if it is paid in 12?
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Answer to a math question 2. A home appliance store sells washing machines with the following conditions: S/. 2,000 as the first payment and 11 additional monthly payments that decrease by 5% each month with respect to the previous payment. If the effective interest is 15% per year, what is the amount to be paid in cash for the purchase of the washing machine? And what is the amount of interest if it is paid in 12?
Esmeralda
4.7101 Answers
1. **Costo inicial y pagos subsecuentes:**
El primer pago es de2000\,\text{soles}
P_n = 2000 \times (1 - 0.05)^{n-1}, \, \text{donde } n = 1, 2, \ldots, 12.
Calculamos los 11 pagos restantes:
P_2 = 2000 \times 0.95, \, P_3 = 2000 \times 0.95^2, \, \ldots, P_{12} = 2000 \times 0.95^{11}.
La suma total de los pagos es el valor presente de una serie geométrica de razónr = 0.95
T = \sum_{n=0}^{11} 2000 \times 0.95^n = 2000 \left(\frac{1 - (0.95)^{12}}{1 - 0.95}\right).
T \approx 19,416.08\,\text{soles}.
2. **Calcular el valor presente de los pagos:**
Utilizando el interés efectivo anual del 15% para calcular el interés mensual:
i = (1 + 0.15)^{1/12} - 1 \approx 0.011645.
El valor presente de los 12 pagos es:
V = \sum_{n=1}^{12} \frac{P_n}{(1+i)^n} \approx 13,832.16\,\text{soles}.
3. **Calcular el monto de intereses:**
Por lo tanto, el monto de interés es
I = T - V \approx 19,416.08 - 13,832.16 = 5,583.92\,\text{soles}.
La respuesta final es que el valor a pagar al contado es aproximadamente13,832.16\,\text{soles} 5,583.92\,\text{soles}
El primer pago es de
Calculamos los 11 pagos restantes:
La suma total de los pagos es el valor presente de una serie geométrica de razón
2. **Calcular el valor presente de los pagos:**
Utilizando el interés efectivo anual del 15% para calcular el interés mensual:
El valor presente de los 12 pagos es:
3. **Calcular el monto de intereses:**
Por lo tanto, el monto de interés es
La respuesta final es que el valor a pagar al contado es aproximadamente
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