## Understand

Present value (PV) or discount value is used to describe a current worth of an amount that will receive at a future date. It is an important concept used in time value of money.

## Example

The formula to calculate the present value of a certain amount is:

PV = FV/ (1+r)^{n OR}_{ }FV(1+r)^{-n}

Where,

PV = Present Value

FV = Future Value

r = Discount Rate or Required Rate of Return

n = Number of Period

For example, you want to deposit a certain sum of money today in saving account to get $1,500 after 5 years. Currently, a bank offers a compound interest rate of 8% per annum. How much money will you need to deposit today?

__Solution__

PV = 1,500(1+0.08)^{-5 }= 1,020.87

Present value (PV) of $1,020.87 means that you will have to deposit that amount to get $1,500 after 5 years.

## Importance

PV is a tool to evaluate two options and get a quantifiable comparison like whether to get a certain amount today or in future. For example, you have two options: Option 1, get $1,000 right now and deposit in saving account of a bank at a rate of 5% per annum or Option 2, get $1,200 after 1 year. By calculating PV, you can easily choose the most suitable option like in the above case PV of $1,200 will be:

PV = 1,200(1+0.05)^{-1 }= 1,142

You should choose for option 2 in which you will get $1,200 after 1 year because it has greater PV than $1,000 in option 1.

PV is also used to calculate the present value of annuities, stock pricing, bond pricing and financial modeling etc.