## Present Value and Present Value Factor

**[Watch video for detailed explanation of concept, formula with examples]**

We define present value as follows:

“The amount to be invested today (present value) at a given rate over specified period to equal the future amount”.

As we are used compounding to find the future value, we use discounting to find present value.

From the formula we studied for future value or accumulated value, we can easily derive equation for present value. The formula for calculating present value is

Where,
*C* is the required future value, *i* is the interest rate for a time
period and *n* is the number of time periods in which we should get the
future value.

The term is called the discount factor or present value factor (*PVF _{i,n}*) of a lump sum 1. It is a common practice in subjects like actuaries to denote v = 1/(1+i). The present value equation can be written in terms of

*PVF*and v as given below:

_{i,n}This is useful as the present value factor is available in present value table for interest rate i and number of periods n.

#### Numerical Problem

Q. 1. If you won a lottery for Rs. 10 lakh. The lottery company offers two options. i) Give full amount of Rs. 10 lakh after 2 years and ii) Give 5 lakh after 1 year and remaining 5 lakh after 3 years. Which option will you take? (interest rate i = 10% pa)

**[Watch Video for solution of this question] **