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The Math of Financial Independence – What is Required to Achieve It? Thumbnail

The Math of Financial Independence – What is Required to Achieve It?

We define financial independence as the point when you can sustain the lifestyle you want based on the wealth you have accumulated. In other words, the point when work becomes optional. That sounds great in theory, but what is required to achieve it?

In this post, we dive into the numbers to help you understand what type of saving behavior is necessary to achieve financial independence earlier than the traditional retirement age. Keep in mind these numbers and calculations are rough approximations and are intended for illustrative purposes only. With that in mind, here is a three-step process to help you figure out how much you must save to achieve financial independence at the age you envision.

Step #1: Figure Out Your Expenses

The first step is to estimate what your annual expenses will be to sustain the lifestyle you desire. Be sure to consider how your activities could change when you have more free time on your hands. Perhaps you will travel more often or pick up new hobbies and interests. These pursuits would bring additional costs, so add them to the equation. Your non-discretionary expenses will also change. On one hand, some new expenses (such as additional healthcare costs) may be added, while on the other hand, some current expenses (such as a mortgage or childcare) may phase out. Lastly, make sure you have a way to account for lumpier, one-off expenses, such as buying a new car, making home improvements, or paying for a future wedding.

Step #2: Apply The 4% Rule to Figure Out Your “Number”

There is a rule of thumb, based on studies looking at historical stock market returns, that states you can withdraw approximately 4% of the initial value of your portfolio, year after year, over long periods of time without running out of money. There is no guarantee that future market returns will ensure the 4% rule persists, but it’s a reasonable approximation. For the purposes of this exercise, take the estimated annual expenses you determined in step #1 and multiply them by 25. This is roughly the size of the investment portfolio required for you to achieve financial independence, assuming there are no contributions from other income sources, such as rental property, a pension, or social security.

Step #3: Choose Your Timeline and Calculate How Much You Need to Save

Next, decide at what age you would like to become financially independent and assume a rate of return for your investments. This will allow you to calculate the amount you must save each year toward the goal of financial independence.

When thinking about what rate of return to use, keep in mind that stocks have historically produced real returns of approximately 7% annually, while bonds have returned around 2% annually. A real return is simply the investment return of a stock or bond, minus inflation. Depending on what percent of your investments you plan to put in stocks versus bonds, your assumed rate of return will vary along the 2-7% spectrum. While future returns are never guaranteed, for our purposes, we will use 5% as a reasonable assumption.

Here’s an example to demonstrate the calculation. Assume you have accumulated $1,000,000 already and your “number” from step #2 is $3,000,000. You want to reach that in 10 years and are assuming 5% as your real investment return. Using an Excel spreadsheet, enter the following inputs:

To solve for PMT:  =PMT(RATE,NPER,PV,FV,1) then hit “Enter”

Using the assumptions above, you would need to save approximately $104,000 annually to achieve your financial independence goal. Keep in mind there are other variables, such as taxes and sequence of investment returns, that go into the actual calculation, but this is a good start.

The Three-Step Process in Action

Let’s say there is a 30-year-old physician who wants to become financially independent at age 50 and spend $150k annually. To achieve this, the doctor would need an investment portfolio of $3,750,000 ($150,000 x 25) at age 50. Starting today, the doctor must save approximately $115k annually for each of the next 20 years and earn a consistent real investment return of 5%. Assuming an annual income of $300k, the physician’s savings rate would be approximately 40%, which is dramatically higher than the mid-single-digit savings rate for the average American, but this is what is needed to reach the goal.

To give you a sense of how the math changes with different assumptions, we can look at a couple alternative scenarios for this same physician. If the goal was to reach financial independence at 45 rather than 50, this individual would need to save around $175k annually (a 60% savings rate). If, on the other hand, this doctor wanted to spend only $100k annually in retirement (rather than $150k), the required annual savings would fall to around $75k (a 25% savings rate).

But Those Savings Rates Are Really High!

If it seems challenging to hit those savings targets, you have a few options:

  • Adjust the age at which you plan to become financially independent
  • Earn more
  • Spend less

These are all areas where you have at least some degree of control, and ideally, you would do a combination of all three. Achieving financial independence earlier than the normal retirement age typically requires some sacrifice to current lifestyle. Everyone is different and must weigh the trade-offs for themselves to determine if the sacrifice will be worth it.

One variable we didn’t mention is assuming higher investment returns. While you can put a larger percentage of your investments in stocks, which tend to produce higher returns over long periods of time, you have no control over your actual investment returns. Therefore, we recommend focusing on what you can control and then adjusting if you end up with higher than expected investment returns, rather than planning for higher returns and never achieving them.


Pursuing financial independence earlier than the average American isn’t necessarily right or wrong. Different people place different significance on the value on spending today versus saving more aggressively to have flexibility in the future. By going through this three-step exercise, hopefully you have a clearer sense of what’s required to reach financial independence and can better evaluate the associated trade-offs.


About MD Wealth Management: We are an Ann Arbor financial planner that specializes in providing financial planning for physicians and retirees. We are CERTIFIED FINANCIAL PLANNER™ professionals and fiduciary financial advisors who operate on a fee-only basis, which means we do not sell financial products or collect commissions. As an Ann Arbor financial advisor, we enjoy working with clients both locally and remotely.