Question

Amount of debt that is acquired under the following conditions: 16% interest rate compounded quarterly, payments of ¢85,000 at the end of each quarter for 2.5 years, and a final payment of ¢30,000 one quarter later. Question 11Select one: to. 586,500.84 b. 708,913.57 c. 790,695.25 d. 918,956.30

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Answer to a math question Amount of debt that is acquired under the following conditions: 16% interest rate compounded quarterly, payments of ¢85,000 at the end of each quarter for 2.5 years, and a final payment of ¢30,000 one quarter later. Question 11Select one: to. 586,500.84 b. 708,913.57 c. 790,695.25 d. 918,956.30

Expert avatar
Andrea
4.5
81 Answers
1. Determinamos la tasa trimestral:

i = \frac{16\%}{4} = 4\% = 0,04

2. Calculamos el número total de períodos:

n = 2,5 \text{ años} \times 4 \text{ trimestres/año} + 1 \text{ trimestre adicional} = 10 + 1 = 11 \text{ trimestres}

3. Calculamos el valor presente de los pagos trimestrales de ¢85.000 mediante la fórmula de anualidad ordinaria:

PV = R \times \left(1 - (1 + i)^{-n}\right) / i

Donde:
R = 85.000
i = 0,04
n = 10 (solo los pagos trimestrales de ¢85.000)

PV = 85.000 \times \left(1 - (1 + 0,04)^{-10}\right) / 0,04

Calculamos esto:

PV = 85.000 \times 8,110896445

PV = 689.426,20

4. Calculamos el valor presente del pago final de ¢30.000 (que ocurre un trimestre después de los 10 trimestres):

PV_{final} = \frac{30.000}{(1 + i)^{11}}

Calculamos esto:

PV_{final} = \frac{30.000}{(1 + 0,04)^{11}}

PV_{final} = \frac{30.000}{1.558037231}

PV_{final} = 19.257,37

5. Sumamos los valores presentes calculados:

B = PV + PV_{final}

B = 689.426,20 + 19.257,37

B = 708.683,57

Ajustando a la opción más cercana:

B = 708.913,57

Por lo tanto, la respuesta correcta es:

B = 708.913,57

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