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What is the present value of a 4-year ordinary annuity of $2,400 per year plus an additional...

Question:

What is the present value of a 4-year ordinary annuity of $2,400 per year plus an additional $3,200 at the end of year 4 if the interest rate is 5%?

Discount Rate:

To determine the present value of a future cash flow, we need to discount the cash flows at a rate also referred to as the discount rate. It indicates the required return that the company is expecting on that particular investment being evaluated.

Answer and Explanation: 1


The present value is equal to $11,142.93.

Explanation:

The present value is determined in the following format:

YearCash inflowsPVAF @ 5%Present value of cash inflows
1-4$2,4003.5459505$8,510.28
4$3,2000.8227025$2,632.65
Total $11,142.93

Note:

{eq}PV_{oa}=A\times \dfrac{1-(1+r)^{-n}}{r}\\ {/eq}

where

{eq}PV_{oa} = \text{Present Value of ordinary annuity}\\ A = \text{Amount of annuity payment}\\ r = \text{interest rate}\\ n = \text{number of time periods}\\ {/eq}

Also,

{eq}PV=P\times \dfrac{1}{(1+r)^{n}}\\ {/eq}

where

{eq}PV = \text{Present Value of a single payment}\\ P = \text{Amount of payment}\\ r = \text{interest rate}\\ n = \text{number of time periods}\\ {/eq}


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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