Finance 101 Archive: Present Value (PV) of a single amount – Formula, Table & Calculator (from 2009) #Finance

ladies and gentlemen welcome to this brief screencast in which we are going to see how to find out the present value of a single amount so let us write down first of all the formula according to the basic mathematical way what we do is we represent the present value by letters PV and in the

subscript we always write a Z and on the right hand side what we are going to write is FV that is future value and in the subscript of that we are going to write n so future value n periods ahead multiplied by this term let us write down the term in square brackets 1 over 1 plus the interest rate

that is K and in um this case when we are finding out the present value this interest rate is also known as the discount rate so this 1 + K is going to be raised to the power of n that is our time periods and we close the bracket you will realize from this formula that this item here 1 / 1 + K to

the^ of n is also known as the present value interest factor of 1 so let us write that here this item here 1 / 1 + K raed to the power of n is known as the present value interest factor of $1 at k% and and time periods um if we want to rewrite this formula now this one here according to the um pvif

format then what we are going to do is we are going to write FV of n just like here so let us copy this and paste it here and what we are going to do with this FV of n is we are going to Simply multiply it by the present value interest factor of $1 at k% for n time periods let us use this formula

now in a simple example suppose uh you have an amount which you are going to receive after 6 years and that amount is going to be $1,000 so since the value of money keeps falling with time let us say that the rate of discount K is equal to 10% so in this set of information what we know is this

$11,000 is our future value six periods ahead time is 6 perience and the discount rate is 10% so let us do that first of all the formula way and then the table way so what we have done here is we have written down this formula here which is the first one here in the mathematical terms and we are

going to Simply substitute our numbers into it for FV of n we write 1,000 and after that inside the bracket what we are going to do is 1/ 1 + K which in this case is 10% so 0.10 and we are going to raise this thing to the The Power of Six because there are six time periods and that’s it now

uh let us use the calculator and find out what is going to be the value of this thing now look at this item in the bracket 1 +10 is going to become 1.10 so let us start using the calculator and see what result we get let us find out what this 1.10 to the power of 6 will be 1.1 to the power of 6

gives us 1.77 1 5 so let us round it off let’s write 1. 772 so inside the bracket here therefore we write 1/ 1.77 2 and after that we say 1,000 * 1/ 1.7 72 let us see how much that is 1/ 1772 is 564 so let’s write that here 0.564 and therefore your present value is $564 it means that if

you invest $564 today at an interest rate of 10% after 6 years it’s going to become $1,000 now if we want to do it the time value tables way we are simply going to write our future value 1,000 and we are going to multiply this by the present value interest factor of of $1 at 10% discount rate

for six time periods and when we go to present value interest Factor tables what we are going to find is that the value of our factor is 0.564 which is the same thing as this thing here so that our answer again here is $564 so that was pretty simple then and that is how we find out the present

value of a single amount bye-bye