The Math Behind the Raise

And why this calculator underestimates your raise's value.

Mathematically speaking, the value of a raise comes from compound interest. In other words, additional money you earn today (or after you complete Fair Pay Academy) grows over time, due to:

  1. Regular salary increases
  2. Investment returns


This calculator takes both of those sources into account, to give you a full picture of how much a raise today can be worth. This article explains how the math behind it works, a few of the model's limitations, and why the value above actually underestimates your raise's true worth.

If you'd like to follow along, you can get out your own calculator - or just keep reading!

1. The Sum of All Raises

Let's look at yearly salary increases first. Analyzing the past 10 years of data from the U.S. Bureau of Labor Statistics Employment Cost Index shows that wages and salaries in the United States have grown by a compound annual growth rate (CAGR) of 3.1% per year (source). If your current salary increases by 3.1% each year, then your raise will, too!

Here's how that looks:

A simple way to understand the value of a raise is just to add up all the values in the Raise column of this table, for each of the years you intend to work. This is called a geometric series, and you can find its sum using the formula:

where:

  • S is the sum of the series,
  • n is the number of years you'll work,
  • a is the amount of the initial raise, and
  • r is the rate at which your salary is expected to increase.


This calculator assumes that you'll work until the age of 65, so n is equal to 65 minus your current age. It also assumes that your salary will continue to increase at 3.1% per year. As a motivated individual equipped with Fair Pay Academy's value-based approach to compensation, however, it's likely your salary may increase by much more!

2. Investment Returns

You could always just save up the extra money your raise generates. If you're really wise, however, you'll invest it.

Say you invest in something relatively safe and predictable, like an S&P 500 Index Fund. It may not be predictable from year to year, but over the past 10 years, that particular index has increased in value by an inflation-adjusted CAGR of 10.3% per year (source). 

What happens if you take the money you get from each year's raise, and invest it until retirement in the S&P 500? 

The math here is a little harder to follow. But we can start with another formula, which gives us the future value of an investment in any number of years:

where:

  • a is the value of the investment,
  • n is the number of years for which it has been invested, and
  • r is the rate of return on investment.


Say you're 30 years old, earn a raise of $10,000, and plan to invest that at a 10% rate of return for 35 years. The value of that raise would be:

 That's a lot of money! And those are only the investment returns on your initial $10,000 raise. So, what you actually want to do is figure out how much each yearly raise will be worth, if you invest it in the S&P 500 until you retire. To do that, you can create a table like this:

Because the rate of investment return is typically higher than the rate of average salary increase - a key factor driving wealth inequality - your raise is actually most valuable now. But it's still going to be worth  a lot in the future, too!

So what the calculator does is simply sum the future values of each year's raise, from now until the time you retire (assuming age 65). And while the table is a nice illustration, it's actually easiest to calculate this with another geometric sequence, that accounts for both the rate of salary increase and the rate of investment return:

where:

  • a is the value of your raise,
  • n is the number of years you'll work (retirement age minus current age), 
  • x is the anticipated rate of salary increase, and
  • y is the anticipated rate of investment return. 


That formula looks complicated! But it has been validated by multiple math PhDs, and if you do the math for yourself using the steps outlined above, you'll see that it all adds up.

At this point, you're probably asking: Can this really be right? Or is it too good to be true?

This model, like any model, has its limitations - and this is a relatively simple model in that it only takes two variables (age and raise size) into account. 

In fact, there are several reasons why this model actually underestimates your raise's true value. Let's take a look.

3. Why This Is An Underestimate

The calculator provides a pretty good estimate. After all, it was designed by math PhDs! 

However, there are a few reasons why this estimate is actually quite conservative. The raise you can earn through Fair Pay Academy may actually be worth much more. Here's why:

  1. You're not average. The calculator assumes that, after your raise, your total salary (and thus the value of the raise) will increase by 3.1% per year, which is the average annual rate of all salaries in the United States over the past 10 years. As someone who has learned Fair Pay Academy's value-based approach to compensation, however, it's likely that your salary will increase much faster - either because you're an above-average worker, or because you earn more raises in the future! After all, what you learn in Fair Pay Academy will serve you for life.

  2. Benefits matter too. The calculator looks only at your salary. But what if your employer contributes a percentage of your salary to a retirement account, which you can then invest? Or what if your Fair Pay Proposal leads to a promotion, which comes with more vacation or better perks? Your salary itself may be your primary form of compensation, but there are others which this model doesn't take into account. And if your benefits aren't great, don't worry - Fair Pay Academy will teach you how to advocate for the benefits you deserve, too.

  3. Your career is about more than money. Fair Pay Academy is about earning a raise, but it's also about maximizing your success at work - and that has other, less quantifiable benefits too. In a role that really utilizes your talents, for instance, you're going to be happier! You'll have greater agency, more influence, and a higher self-esteem. (Not to mention the admiration of others.) These sources of value aren't monetary - so they aren't in the calculator - but they can be hugely important. Your day-to-day satisfaction really matters.


This simple calculator estimates the monetary value of your next raise, not all the ones that follow, nor the social and emotional benefits those entail. And it also fails to capture the intrinsic value of learning an approach that will serve you throughout your career. It's a useful tool, but it's not a full accounting.

And the best part? You can learn the fundamentals of Fair Pay Academy's value-based approach for free, then join our Fair Pay Accelerator for personalized feedback and support, all at no risk to you. (If you complete the Accelerator and aren't fully satisfied, you have 90 days to get your money back with no questions asked.) The value of your raise is in your hands! You just need to reach out and claim it.