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Consider an annuity consisting of three cash flows of $1,500 each. Assume a 6% interest rate....

Question:

Consider an annuity consisting of three cash flows of $1,500 each. Assume a 6% interest rate. What is the present value of the annuity if the first cash flow occurs today?

Annuity:

An annuity is a series of cash flows that are expected to occur periodically. The equivalent present worth or future value at a certain point in time can be figured out by considering the relevant interest rate.

Answer and Explanation: 1

The present value of the two cash flows expected to occur in the future is given by:

{eq}\begin{align*} &= \dfrac{A}{(1 + r)^1} + \dfrac{A}{(1 + r)^2} \\[0.3 cm] &= \dfrac{\$1,500}{(1 + 6\%)^1} + \dfrac{\$1,500}{(1 + 6\%)^2} \\[0.3 cm] &= \dfrac{\$1,500}{(1.06)^1} + \dfrac{\$1,500}{(1.06)^2} \\[0.3 cm] &= $2,750.09 \end{align*} {/eq}

The present value of the annuity is given by:

{eq}\begin{align*} &= \text{Cash flow occurring today + present value of two cash flows expected to occur} \\[0.3 cm] &= $1,500 + $2,750.09 \\[0.3 cm] &= $4,250.09 \end{align*} {/eq}

The calculated present value of the annuity is $4,250.09.


Learn more about this topic:

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How to Calculate the Present Value of an Annuity

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Chapter 8 / Lesson 3
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Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.


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