## Understanding Present Value and How to Solve for it.

In this post we simplify present value time value of money calculations. This is a continuation of our blog posts on understanding the time value of money. If time value of money is a new term for you then check out our first post in this series on the time value of money. In that post we cover the basics of time value of money.

What is the value in today’s dollar of an amount of money that will be received in the future? This is what present value calculations find.

When solving for present value we use the term discount rate instead of annual interest rate because we are discounting a future sum of money back to its present value.

The easiest way to calculate present value is with the time value function on a financial calculator. If you are trying to determine what the present value of \$1,000,000 is that you will receive in 10 years at a 10% discount rate then you would enter the following inputs into your calculator.

FV=1,000,000

I/Y=10

N or Periods = 10

PV=?

Click CPT PV and you should get = -385,543.29. (this answer is rounded to two decimal points)

*Note getting a negative on either PV or FV is normal. Typically if you are solving a Time Value of Money question that includes both PV and FV you have to make one of them negative for it calculate properly. The reason it is like this is because it is showing money leaving your hand as the negative and returning as the positive.

The greater the discount rate is will equal a smaller present value given that everything else is the same between two future value sums of money. For example if the same numbers are used from above, but the discount rate is 4% instead then the present value will be larger.

FV=1,000,000

I/Y=4

N or Periods = 10

PV=?

CPT PV = -675,564.17

If you are wondering how time value of money is affecting your life then consider this- from a practical standpoint understanding time value of money is important in making every basic savings, credit and investing decision. It is key knowing how to create and maintain wealth.

## Basics of Time Value of Money

Money has a time value

The money you have today is worth more than what you have in a year. For example if you were to have \$1500 now it is worth more than \$1500 a year from now because of compound interest. This is dependent on if you taking advantage of compound interest. You have the opportunity to earn interest on money that you have now.

Compound interest is interest that you earn on interest you’ve already earned. For example if you invest a principal (starting amount) of \$100 and you earn 7% in a year on the \$100 investment then you’ve earned \$7. If you choose to reinvest that \$7 of interest then you now have \$107 earning interest for year two. This may not seem like a whole lot, because it is a simplified example. However, consider once you have saved up money and have invested for a few years. Consider if you now have \$100,000 dollars earning 7%. That means in one year you earned \$7,000. Once you reach \$1,000,000 if you are earning 7% that means you are earning \$70,000 and that the next year you now get to earn 7% on \$1,070,000! Compound interest can be your best friend if taken advantage of, the earlier you start using it in life the better!

Compound interest is much like a ball rolling down a hill. Untouched, the further it is allowed to roll the faster and more momentum the ball picks up. Compound interest is the same way! When you add more money to the principal it speeds up the process even more. It is kind of like kicking the ball to speed it up even more once it already has momentum.

Definitions for Time Value Calculations

Present Value is what money is worth now. For example if I have \$150 right now that is its present value.

Annual Interest Rate – if you have an account that pays 5% a year then that is your annual interest rate. If the \$150 that you have earns 5%, then at the end of year 1 you will have earned \$7.50.

Future Value is what the money will be worth at the end of year 1 or at another point in the future. In the example of \$150 at an annual interest rate of 5% the future value after one year will be \$157.50.

When calculating Future Value or Present Value you will also need to know the term or in other words how many times does the interest compound and is it once a year, semi-annually, quarterly, monthly in the time frame that you are calculating. The easiest way to compute a time value equation is to use a time value calculator.

Non-annual compound interest

Non-annual compound interest is when interest compounds on a term that is quicker than a year. It could be semiannually, quarterly, monthly, and even daily. The quicker your money compounds the quicker you earn money on your interest.

To compute non-annual time value equations it is easiest to use a financial calculator’s time value functions.

Understanding time value inputs on a calculator The pictures above display what the inputs will most likely look like on the BA II Plus Texas Instruments financial calculator and on an internet time value calculator. There is also many financial calculator apps available for smart phones. Usually they are no more than a few dollars.

PV or Present Value – is where you input the present value or where the calculation will occur for Present Value

FV or Future Value – is where you input the future value or where the calculation will occur for the future value

The N or Periods – is where you input the number of payments or compounding periods or where the calculation will occur for the periods

PMT or Payment – is where you input how much money is being contributed per period (if money is being contributed) or where the calculation will occur for how much to contribute.

I/Y or Rate/Annual Rate – is where you input what the interest is per term or compute what the interest rate is per term. It is entered as a percentage not a decimal. For example if your annual interest rate is 12%, but it is compounded monthly you would input 1.

If using the BA II Plus Texas Instrument calculator click the “CPT” button and then which ever input you are wanting to find. For example if you are wanting to find present value, once you have inputted the numbers into FV, I/Y, N, and PMT click “CPT” and then click “PV”.

Summary

This blog post is intended give the reader the baseline knowledge of time value of money and compound interest needed to then delve deeper into the topic. The topic of time value of money expands well beyond the scope of this article. We will be adding additional posts on the topic of time value of money in the near future.