Perpetual annuities are a series of payments whose duration has no end. Explain how can we calculate them, if they have no end?



Answer to a math question Perpetual annuities are a series of payments whose duration has no end. Explain how can we calculate them, if they have no end?

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Las anualidades perpetuas son un tipo de acuerdo financiero en el que una serie de pagos continúa indefinidamente, lo que significa que no hay una fecha de finalización especificada. Si bien el concepto de anualidades perpetuas implica un número infinito de pagos, los cálculos prácticos se basan en el supuesto de que los pagos continuarán para siempre. La fórmula para calcular el valor presente (PV) de una anualidad perpetua implica dividir el pago anual (PMT) por una tasa de descuento (r). La fórmula es la siguiente: PV= \frac Dónde: PV es el valor presente de la anualidad perpetua. PMT es el pago anual. r es la tasa de descuento. Esta fórmula se deriva del concepto de valor presente, que refleja la idea de que el valor de los pagos futuros disminuye con el tiempo cuando se descuentan a una determinada tasa. En el caso de una anualidad perpetua, la división por la tasa de descuento supone que los pagos continuarán indefinidamente. Es importante tener en cuenta que las anualidades perpetuas son construcciones teóricas y, en realidad, los pagos verdaderamente perpetuos son raros. La mayoría de los instrumentos financieros tienen una duración finita, pero para simplificar en ciertos modelos financieros, se pueden utilizar las perpetuidades como concepto matemático. En términos prácticos, cuando se trata de instrumentos financieros que tienen una vida útil finita, se utilizaría una fórmula similar para el valor presente de una anualidad ordinaria, que implica descontar cada pago futuro a su valor presente y sumarlos. La fórmula de perpetuidad es una simplificación útil para discusiones teóricas y ciertos modelos financieros.

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