Question

How much must be invested today, March 1, 2024 to make equal quarterly withdrawals due for $2,500 each during 2022, if deposits earn interest at 8% CT?

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Answer to a math question How much must be invested today, March 1, 2024 to make equal quarterly withdrawals due for $2,500 each during 2022, if deposits earn interest at 8% CT?

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Frederik
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100 Answers
Para este problema, utilizaremos la fórmula del valor presente de una anualidad ordinaria:

VP = \dfrac{R \times (1 - (1 + i)^{-n})}{i}

Donde:
- VP es el valor presente total de la anualidad
- R es la cantidad de cada retiro (en este caso $2,500)
- i es la tasa de interés por periodo (en este caso trimestral, es decir 8%/4 = 2% o 0.02)
- n es el número total de periodos en la anualidad (en este caso serán 12 periodos para los cuatro retiros trimestrales de 2022)

Sustituyendo los valores dados en la fórmula:

VP = \dfrac{2500 \times (1 - (1 + 0.02)^{-12})}{0.02}

Simplificando:

VP = \dfrac{2500 \times (1 - 0.8194)}{0.02}

VP = \dfrac{2500 \times 0.1806}{0.02}

VP = \dfrac{451.5}{0.02}

VP = \

Por lo tanto, se deberán invertir \ 22,575 hoy, marzo 1 de 2024 para poder realizar retiros trimestrales vencidos iguales por \ 2,500 cada uno durante 2022 y obtener un interés del 8% CT.

\textbf{Respuesta:} Se deberán invertir \$22,575 hoy.

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