# Present Value of Money

**Definition**

The time value of money concept states that $1 today is worth more than $1 in the future. The reason is rather simple. If you have $1 today, you can invest it and receive more value in the future. So, the present value (PV) of money is the current worth of the amount that will be received at a specific date in the future. It is implied that the money is invested at a specific interest rate called the required rate of return.

Note that the present value is usually less than the future value except during times of negative interest rates!

**Formula**

Calculating the present value is also called discounting and is the reverse of finding future value (FV), which is also called compounding. Furthermore, there is a relationship between the future value and the present value described by the following equation.

Here FV_{N} is a future value at the end of relevant period N, PV is a present value, I represents an interest rate earned per period, and N is a number of periods.

The equation above can be modified to find the PV as follows:

**Graphic Approach**

As was mentioned above, the sum to be received in the future would be worth less than the same sum to be received today. Two drivers decrease the present value of a future amount of money.

**Interest rate**. The higher the interest rate, the faster the present value will decrease.**Number of periods**. An amount of money to be received in the future even at a relatively low interest rate has very little present value.

Thus, the further in the future the due date is extended, the lower the PV will be (gradually approaching zero).

**Examples**

Let’s assume an investor intends to have $100 after 5 years. The money could be invested at a 12.5% annual rate. We need to discount $100 to find how much the money is worth now (zero point). Graphically, the discounting is shown in the figure below.

We start with $100 at the end of the fifth year and get $88.89 worth at the end of the fourth year. Further, we discount $88.89 and get $79.01 at the end of the third year. This process continues for the remaining years until we get the present value of $55.49 at the beginning of the first year (zero point on figure above).

PV _{End of 4th year} = $100/(1+0.125) = $88.89

PV _{End of 3rd year} = $88.89/(1+0.125) = $79.01

PV _{End of 2nd year} = $79.01(1+0.125) = $70.23

PV _{End of 1st year} = $70.23(1+0.125) = $62.43

PV _{Beginning of 1st year} = $62.43(1+0.125) = $55.49

The step-by-step approach demonstrated above is cumbersome, especially for a large number of periods. So we can reach the same result using the formula of PV mentioned above.

**Calculator and Discount Table**

You can also find the present value of money using our online __calculator__ or __discount table__.