An Economics Fundamental: The Time Value of Money


Earlier in the week, I talked about how you need to spend your time and money wisely since both are valuable. That idea stems from a fundamental economic concept: Time Value of Money (TVM).   TVM plays a crucial role in all finance theory.  As such, I thought we should explore the concept a little deeper.

What is the Time Value of Money?

TVM states that money you have now is worth more to you than that same amount in the future because you can invest that money to make even more. In short, it’s better to have money now, rather than later.

To make the concept more concrete, if you have a $1000 today, and you can find an investment vehicle that earns you 10% a year, you will have $1,100 a year from now. On the other hand, a $1000 a year from now, at the same 10% interest rate, is only worth $909 today.

So in this context, time is literally money.

The Components

You will find TVM everywhere in your daily life, especially when you become aware of it. It determines how much you pay on your mortgage, how much an investment like a stock or bond may cost you, and why your $189 million winning lotto ticket will only net you $130 million cash prize.

Every TVM problem contains five variables: present value (PV), future value (FV), number of periods (n), interest rate (i) and payment amount (PMT).

Here are some simple definitions:

  • Present Value: The amount you have today
  • Future Value: The amount you have at some point in the future
  • Number of Periods: The amount of time an investment is held
  • Interest: the charge for borrowing money
  • PMT: a series of equally spaced payments

TVM problems usually involve solving for one of these variables by using the other four. And while TVM formulas can get extremely complex, I just want to start off by breaking down the examples I used earlier.

The Formulas

To find the future value of a lump sum, you can use this formula: FV=PV(1+r)^n.

Accordingly, to find the present value of a future sum, you use this formula: PV=FV/(1+r)^n.

You’ll notice that neither equation contains the PMT variable. That’s because this example assumes no payments (or cash flows). In other words, PMT is zero.

So in my $1000 example, the numbers breakdown like this

FV = 1000(1+.10)^1 = $1,100

PV = 1000/(1+.10)^1 = $909

What does this mean for you?

I know that this information seems a bit technical. And with the various calculators and spreadsheets, you will likely never do these calculations longhand.

However, I think it’s important for you to understand how the different components of the TVM formula work, so you can better grasp tougher concepts like bond pricing, stock valuation, and annuity payments. In addition, you’ll have a better understanding of how to chose investment vehicles when you can find their true value either now or in the future.

I want to empower you as a participant in personal finance. And understanding concepts like this will help make you more confident with your money. The more confident you are, the better you will handle your finances.