# How to retire early with the help of math

Here’s a question: If you continue your current saving and spending habits, how long will it take you to accumulate enough money to live off of your savings alone?

Let’s refer to this magic number as the financial independence (FI) number. Calculating your FI number seems like a daunting task, which is why I devote an entire section of The Calculus of Happiness (Section 3.3) to discussing the concepts involved, the ultimate formula, and the insights the formula yields. The calculator below let’s you calculate your own FI number (the calculator is based on equation (3.17) in The Calculus of Happiness). To use the calculator, you’ll need to input the following quantities into the  green cells:

• Your yearly savings: how much you save (or plan to save) each year
• Your yearly total expenses: all of your income and earnings minus the yearly savings amount. (Note: this calculation of “total expenses” is meant to include all of your expenses, including taxes, discretionary spending, etc.)
• Your current savings (this could be \$0)
• Finally, the annual rate of return (expressed as a decimal) you expect to earn on your accumulated savings once you officially retire

After inputting these values, the calculator will output the FI number (in years).

It’s important to mention that the calculator below makes several simplifying assumptions. These are discussed in Section 3.3 of The Calculus of Happiness, and briefly summarized in the Limitations section below. (I discuss in the book how the FI number might change if those assumptions don’t hold.) But more important than those assumptions (since they’re fairly realistic assumptions), is the main insight that emerges from the analysis of the FI equation: the fastest way to reach financial independence is to increases the ratio of your savings to total expenses. (I call this the STE ratio in the book.)

## Limitations

This calculator makes the following assumptions:

• You save the same amount each year
• Your savings are invested (and earn the annual return inputted into the third green cell in the calculator above)
• You currently have some amount saved that’ll also be invested earning the
same annual interest rate. (Note: that amount could be zero.)
• Your yearly expenses stay the same
• You have no other assets you can sell–no home, no car–or future
sources of income (no retirement account, no Social Security, etc.)

These assumptions aren’t exactly 100% realistic. However, they’re fairly realistic (for example, most people don’t experience wild swings in their yearly spending and saving).