Present Value Formula
As with future value, there is a formula for calculating present value. Shown below is the formula. It looks very similar to future value because it is the future value formula, rearranged to provide an expression for present value.
|PV=FV [1/(1+ i)n]|
|PV= Present value
Present value is the amount we don't know. This is the value we will solve for in our calculations. It's the amount we need today to achieve a determined future goal.
|FV= Future value
Future value is the amount of money we want in the future. It is the amount that will be reduced at a determined interest rate to calculate the present value.
|i= interest rate
Interest rate has a great effect on present value. The interest rate in our formula must be written in decimal form: for example, 3% is 0.03.
|n= number of interest payments during a specified time
n indicates the number of times interest is applied.
Start With the Variables
Let's begin with the first question we asked earlier. In the future value lesson, we figured out a number of ways to save for the future… for a wedding, for a house, and determining how much that 10K windfall from grandma would grow. Those are all very important events in your life to save for and should be top priorities, but what about saving for the things you've only dreamed about!
|In the Dog House…|
Looking into the future, you know you'll get married and buy a house. Life will be good! But, for as long as you can remember, you've dreamed of having a pure-bred English bull dog. You've already named her – Lu Lu! Your parents won't buy you one because, today, they cost about $3,000. If you buy the dog soon after you get married, about 15 years from now, you've determined that the future value of $3,000 (counting on a 3% inflation rate) is $4,674.You have $10,000 from your grandmother. How much of it do you need to put into the bank today in order to have $4,674 (enough to buy your sweet Lu Lu) 15 years from now? Your bank is paying 4% interest on savings accounts.
To know how much to put aside for Lu Lu, we have to replace the variables in the present value equation with the figures related to purchasing Lu Lu. Do you know what values to replace FV, i, and n with? Enter your answers in the text boxes below. Click reveal answer to see if you are correct.
PV= [1/(1+ ) ]
PV=4,674[1/(1+ .04 ) 15 ]
Do your values match ours?
- $4,674 is the future value because that's how much money we want to have at some point in the future.
- 4% is our interest rate, so we write this as .04. (If you mistakenly input "4" instead of ".04," don't worry about it; just keep this in mind for future calculations.)
- Finally n=15 because n represents the number of times interest will be applied; it is also the number of years we plan to save.
Now, on to Calculation
OK. Let's walk through the steps of calculating this out. Click here to view the demonstration.
On the Calculator
We performed the above calculation "behind the scenes," but if you'd like to see how we do this on a calculator (exponents can be tricky), Click here to view a video demonstration.