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17 November, 07:18

You are comparing two annuities. Annuity A pays $100 at the end of each month for 10 years. Annuity B pays $100 at the beginning of each month for 10 years. The rate of return on both annuities is 8 percent. Which one of the following statements is correct given this information

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  1. 17 November, 07:31
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    The list of statements to answer this question is:

    A) The future value of Annuity A is greater than the future value of Annuity B. B) Annuity B will pay one more payment than Annuity A will. C) Annuity A has a higher future value but a lower present value than Annuity B. D) Annuity B has both a higher present value and a higher future value than Annuity A. E) The present value of Annuity A is equal to the present value of Annuity B.

    Answer:

    D) Annuity B has both a higher present value and a higher future value than Annuity A.

    Explanation:

    To calculate the present value of an annuity, you must discount each future cash flow, each according to the number of periods that correspond to it, counting from the current date.

    The present value of an annuity depends on: the amount of the cash flow (montly payment), the moment when each cash flow is paid, the number of periods, and the rate of return.

    For this question, the two annuities pay the same amount ($100), the number of payments is the same (the product of ten years by the number of payments every year: 10 * 12 = 120), and the rate of return is the same (8%).

    What is different is that annuity B starts paying one month earlier then annuity A.

    Since, the stream of cash flows of annuity A is one month further in time than that of annuity B, the present value of each cash flow from B is less than the present value of the corresponent cash flow from B.

    Hence, the present value of annuity B is higher thant the present value of annuity A.

    The future value can be calculated using the present value and the formula Future value = Present value * (1 + r) ⁿ. Since, the present value of annuity B is higher, its future value will be higher too.

    Therefore, you conclude that annuity B has both a higher present value and a higher future value than annuity A.
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Home » Business » You are comparing two annuities. Annuity A pays $100 at the end of each month for 10 years. Annuity B pays $100 at the beginning of each month for 10 years. The rate of return on both annuities is 8 percent.
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