Calculate your FIRE Age (Financial Independence/Retire Early)

Thinking about retiring early? Here’s my ???FIRE??? (Financial Independence/Retire Early) Age Calculator! It will tell you how long you can live off your assets if you stopped working at a certain age. If your investment growth is greater than your expenses, then you are financially independent. My approach assumes that your lifestyle does not change, as do all the other calculators out there. This is unlikely to be true, but it gives us a current snapshot of where you’re headed.

Here’s the Excel version:

FIRE.xls

My calculator outputs these results:

• If you quit your job now, how long you will survive on your current net worth
• If you continue to work additional years, how long you will survive on that accumulated net worth
• Present value of retirement net worth
• Future value of retirement net worth

You will need to calculate these inputs on your own:

• Current Net Worth
• Current Average Monthly Income (After tax)
• Current Average Monthly Expenses
• Current Age

I personally use year-to-date sum of income and expenses to get my current averages. It’s up to you if you want to consider your real estate in the net worth calculation. Use what makes sense for you. The net worth should be the amount of assets you can use to live off of, including the value of your pensions. If you can guesstimate the present value of your social security income, that would help make this more accurate, but that is difficult.

Assumptions

• Constant Annual Investment Yield (you can adjust this, and you should use your own portfolio’s performance)
• Constant Annual Inflation Rate (you can adjust this)
• Your income and expenses increase only by the inflation rate
• When you retire, you withdraw only the amount of expenses you need while the rest of the portfolio grows

How to Calculate Your Retirement Age

Now the fun part! Just adjust the number of Work Years to choose when you retire, then see how long you’ll survive based on your accumulated income. When “Survive to” becomes infinity, that means your investment gains have exceeded your expenses, so your net worth will continue to grow forever. Play around with the number of years worked until you hit the sweet spot right before you hit infinity. You might be able to use the Solver Add-on to help you here, if you are savvy enough to configure it.

For example, given the default inputs of:

• Yield 7%
• Inflation 3%
• Net Worth 50,000
• Monthly Income 4,000
• Monthly Expenses 3,000
• Current Age 25.25
• Work Years 17

If you quit now, you will have enough money to live off of until 26.68 on your current net worth and expenses. If you work another 17 years, you will have enough money to live off of until 55.89.

The present value of the money you need to retire on is $648,204. If you won the lotto or inherited that amount today, you can retire now. The future value of the money needed is $2,047,559. As you work and accumulate savings and grow your investments, you can retire when you’ve got the $2.05 million 17 years in the future.

If you bring the number of years worked up to 32.5, you’ll find that cusp where you become financially independent. So this person needs to work until 57.75 to retire early.

The wording “Survive to” is correct. The moment you hit that age you will ???DIE IMMEDIATELY???.

The Math

Ok, now here is the real fun part!!! Because I want to consider an increasing amount of cost of living and increases in income for inflation, this will be a non-level annuity. So we’ll use the geometric progression formula. It looks like this:
PV is present value of the payments, P is payment, n is the number of periods, i is the yield rate, and g is the growth rate. This formula is saying your payments grow by the amount of (1+g) each period (hence non-level). Since we’re looking at monthly amounts, the monthly effective rates will be (1+i)^(1/12)-1. Your “payments” are the expenses being pulled out of your present value net worth. Discounting all future expenses, this gives you the present value of your required net worth to survive for n periods. Solving for n:

This helps us solve for your survival length if you quit your job right now. PV is your current net worth, g is the inflation rate. But how about if you wanted to work more? You’ll need to consider the present value of your future income to add to your current net worth, then use that sum as your starting point net worth. This is equivalent to earning out your income and subtracting expenses year after year, because math is beautiful like that.

Here is the check:

You start with $1,500 net worth, have $1,000 annual income, $600 annual expenses, your investment yield is 7%, and inflation is 3%. The Work column continues to add income for the next 10 years you work, and expenses continue on after retirement. The Lump Sum column is taking the PV of future income and just subtracts expenses over the years.

The question I had was, will taking a present value lump sum of future income give you an equivalent  survival date as if you were working over time? I wasn’t sure if the investment yields would work out right, and I wanted a brute force way to be sure my formula gave the correct answer. And it did! After the 10th year of income, the account balances become equivalent. The calculated survival age is 25.96. Math is beautiful.

So what exactly causes the infinity? It’s the result of logging a negative value in the n formula.

Simplifying, you get Financial Independence if: