# Present Discounted Value Formula

Before learning what is the present discounted value formula, let us recall what is a discount. Discount refers to the price lower than the actual price of the commodity. The present discounted value formula is used to find the present discount value against a particular future amount received in a year from the current date.

## What is the Present Discounted Value Formula?

The present discounted value formula is represented in terms of the future value, rate of return, and the number of periods. It is given as:

\(PV= \dfrac{FV}{(1+r)^n}\)

Where,

- PV = present value
- FV = future value
- R = rate of return
- n = number of periods

Let us see the applications of the present discounted value formula in the following section.

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## Examples Using Present Discounted Value Formula

**Example 1:** What is the present value of $500 received in 3 years if the rate of interest is 10% per annum discounted annually?

**Solution:**

To find: The Present Value.

Given,

Future value = $500

Time = 3 years

Rate = 0.10

Using present discounted value formula,

\(PV= \dfrac{FV}{(1+r)^n}\)

\(PV= \dfrac{500}{(1+0.10)^3}\)

\(PV= 375.66\)

**Answer:** The present value is $375.66.

**Example 2**: What is the present value of $500 received in 3 years if the rate of interest is 10% per annum discounted semi-annually?

**Solution:**

To find: The Present Value

Given,

Future Value = 500

Time = 3×2 = 6 months (as the rate is discounted semi-annually)

Rate = 0.10

Using present discounted value formula,

\(PV= \dfrac{FV}{(1+r)^n}\)

\(PV=\dfrac{500}{(1+0.10)^6}\)

= 282.24

**Answer: **The present value is $282.24

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