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By participating in a savings program that offers a monthly interest rate of 0.5%, how much would accumulate at the end of 3 years if a monthly deposit of $200 is made?

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Answer to a math question By participating in a savings program that offers a monthly interest rate of 0.5%, how much would accumulate at the end of 3 years if a monthly deposit of $200 is made?

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Clarabelle
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77 Answers
1. Determinar el número de periodos, ya que el interés es mensual y el tiempo es en años:

n = 3 \, \text{años} \times 12 \, \text{meses/año} = 36 \, \text{meses}

2. Calcular la tasa de interés mensual en decimal:

i = \frac{0.5}{100} = 0.005

3. Aplicar la fórmula del valor futuro de una anualidad (depósitos periódicos):

FV = P \left( \frac{(1 + i)^n - 1}{i} \right)

donde:

P = 200 \, \text{dólares/mes}

i = 0.005

n = 36 \, \text{meses}

4. Sustituir los valores en la fórmula:

FV = 200 \left( \frac{(1 + 0.005)^{36} - 1}{0.005} \right)

5. Calcular el valor futuro:

FV \approx 200 \left( \frac{(1.005)^{36} - 1}{0.005} \right)

FV \approx 200 \left( \frac{1.19668 - 1}{0.005} \right)

FV \approx 200 \left( \frac{0.19668}{0.005} \right)

FV \approx 200 \left( 39.336 \right)

FV\approx7867.22

Por lo tanto, al final de 3 años se acumulará aproximadamente 7867.22 dólares.

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