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How to Calculate the Present Value of a Single Amount

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Question: How to Calculate the Present Value of a Single Amount

There are three approaches to solving the problem of calculating the present value of an single amount, one type of time value of money calculation. First, you can use the present value of a single amount formula. Second, you can use a financial calculator. Just about any financial calculator will do and will follow just about the same steps. Third, you can use a spreadsheet application, such as Excel. We will explore all three approaches.

Answer:

The Problem and The Formula

The first thing to remember is that present value of a single amount is the exact opposite of future value. Here is the formula:

PV = FV [1/(1 + I)t]

Consider this problem:

Let's say that you have been promised $1464 four years from today and the interest rate is 10%. The year (t) is year 4. We want to know what that $1464 is worth today (the present value) given that the interest rate is 10% and the year is 4. Using the present value of a single amount formula, we can calculate the present value of $1464 if the interest rate is 10% at the end of 4 years using the formula:

PV = 1464 [1/(1 + .10)]4 = $1,000

Calculating present value is called discounting. Discounting cash flows, like our $1,464, simply means that we take inflation and the fact that money has the ability to earn interest into account. Since you do not have the $1,464 in your hand today, you cannot earn interest on it so it is discounted today.

Clearly, using the formula is the long way to do present value problems. Using a financial calculator or a spreadsheet application is a more efficient way to calculate present value.

Present Value of an Single Amount Using a Financial Calculator

You can find the present value of a single amount with any calculator with an exponential function, even non-financial calculators. It is best to use financial calculators because they have five keys that correspond to the five variables in time value of money equations. This present value of a single amount equation that we calculated above uses only four of those variables. Look at your financial calculator. Here are the key and inputs that you punch:

Punch N and 4 (for 2 years)

Punch I/YR and 10 (for the interest rate of 5%)

Punch FV and 1,464 (for the amount of money we are calculating interest on in year 4)

Punch PMT and PMT (there are no payments beyond the first one)

Punch PV and you will have your answer of $1,000

Present Value of a Single Amount Using a Spreadsheet

Spreadsheets, such as Microsoft Excel, are suited for calculating time value of money problems and other mathematical functions. The function that we use for present value of a lump sum on an Excel spreadsheet is:

PV(rate,nper,pmt,fv,type) OR

=PV(0,10,4,0,1464,0)

Specifically, you go to an Excel worksheet and click on Financial function. You will pull down a menu and click on PV. That will open a box and you will fill out the information for the problem you are trying to solve. In the example we are using, you fill out the interest rate of 0.10, the time period of 4 (year), payments of 0, future value of $1464 expressed as a positive number, and a 0 for the last item which means that any payment would be at the end of the time period if we had payments. You end up with the function above. Then, you go to the right-hand side of the worksheet at the top and click on Calculate. You will get the answer of $1000.

This video lesson will help you with practicing calculations for present value of a single amount.

These are the three ways to calculate present value of a single amount.

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