Question

A family buys a house that costs $4,000,000.00, pays $1,000,000.00 in cash and obtains a 30-year mortgage to pay the difference at 8% monthly convertible interest. What is the value of your monthly payments?

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Answer to a math question A family buys a house that costs $4,000,000.00, pays $1,000,000.00 in cash and obtains a 30-year mortgage to pay the difference at 8% monthly convertible interest. What is the value of your monthly payments?

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Dexter
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Una familia compra una casa que le cuesta $4,000,000.00. Pagan $1,000,000.00 en efectivo y obtienen una hipoteca a 30 años para pagar la diferencia a 8% de interés convertible mensual. ¿Cuál es el valor de sus pagos mensuales?

[SOLUTION]

P = 24,322.84

[STEP-BY-STEP]

1. Determinar la cantidad del préstamo:

4,000,000 - 1,000,000 = 3,000,000

2. Convertir el término del préstamo a meses:

30 \times 12 = 360

3. Calcular la tasa mensual de interés:

\frac{8\%}{12} = 0.67\% = 0.0067

4. Usar la fórmula de pago mensual de una hipoteca:

P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}

Donde:
- P es el pago mensual.
- PV = 3,000,000 es el monto del préstamo.
- r = 0.0067 es la tasa de interés mensual.
- n = 360 es el número de pagos.

5. Sustituyendo los valores:

P = \frac{0.0067 \cdot 3,000,000}{1 - (1 + 0.0067)^{-360}}

6. Calcular los valores dentro de la fórmula:

P = \frac{20,100}{1 - (1.0067)^{-360}}

7. Calcular la parte exponencial:

1 - (1.0067)^{-360} \approx 0.891

8. Finalmente:

P = \frac{20,100}{0.109} \approx 24,322.84

Respuesta:

P = 24,322.84

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