Valor Futuro de una Anualidad Anticipada - Clase 17 - Matemáticas Financieras

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Eduardo Aponte, and we're going to study financial mathematics. Welcome! Future Value of an Annuity [Music] Due. In the previous lesson, we saw that the difference between ordinary and due annuities lies in the fact that due annuities have the payments made at the beginning of each period. Regarding the formula for present value and future value of an annuity, we

only need to multiply by 1 + I to obtain the formulas for present value and future value of an annuity due. The future value formula is this, and multiplying by 1 + I, we get this: the future value formula for an annuity due, where bf is the future value, a is the value of the annuity, i is the

periodic interest rate, and n is the number of periods or term. Now then... We have the formula, let's see an example. How much money will be obtained if 120 is invested monthly in an investment fund for 3 years starting from today, if they pay an interest rate of 1.5 per month? The following is the cash flow.

The horizontal line is the timeline and each arrow indicates a cash flow. Zero indicates the beginning, and 1, 2, 3, etc., indicates the end of each period. In this case, 34 indicates the end of the 34th month, as well as marking the beginning of the 35th period or month. In this case, substituting into the formula,

we have that the future value is equal to 120m times 1 + 0.015, which is equivalent to the interest rate of 1.5 per month raised to the 36th power, which is the number of periods in 3 years. -1 divided by 0.015 multiplied by 1 + 0.015 equals 5758. The above means that if