Why 2% is Such a Big Number

The average American spends 94.6% of their income every year.  This means the average American saves only 5.4% of their income!  I’m going to show you how much impact the tactics of using a rewards credit card (that I showed you last post) can change your savings and life.

I’m going to present two cases to you and demonstrate the long term effects.  Case One: You use cash and debit cards for your spending and save the average American amount of your income (5.4%). Case two:  You use your 2% rewards credit card for spending, with the rewards earned invested forever.  You save the average American amount of your income (5.4%) plus your rewards from your 2% cash back credit card.

First things first, I need to talk about my assumptions that I’m making for this exercise.  My engineering professors would be so pleased with me right now.

ASSUMPTIONS

  1. Over the long term, your investments are going to make 7% a year. Some years better some year worse. This is considered your compounding rate.
  2. Inflation is going to chew up 3%, leaving you with a real gain of 4%. This 4% is considered your safe withdrawal rate.
  3. You’ve won the game and are financially independent (you do not have to rely on any particular job for income) when your investments are equal to your expenses divided by your safe withdrawal rate. This means your investments income is greater than your expenses. You should know your expenses because you’ve been tracking them on your balance sheet, right?
  4. You have a constant savings rate. In reality nobody gets paid the same amount and saves the sames amount throughout their life, but seriously the math turns into calculus if I don’t make this assumption.

These are rough assumptions and we could debate them all day, but they work for getting my point across.

So to put this into terms everyone can relate to I’m going to measure everything in years that it takes you to reach financial independence. The point where your investment makes as much money as it costs you to operate your life style at your current efficiency levels.

The math involves solving for the future value of a normal annuity (a fixed amount of money) where the future value is set to the amount of money you need to be financially independent.

Here is the formula for the future value of a normal annuity

Normal Annuity

Now here is what that formula looks like when we substitute in our variables.

Sub in our variables

We can also substitute our variable in for the amount of money needed to be financially independent by taking 1 minus our savings rate, which is equal to your expenses rate. You are either spending money or saving money. The expenses rate divided by your safe withdrawal rate gives us the total assets needed to be financially independent. Here is what that formula looks like.

sub in assets

 

And now by the power vested in me by my TI-89 we can solve for Years. Here is what the final formula looks like.

Sub final

Here are the results for the cases using the above formula.

CASE 1 (Cash or Debit Card)

Case 1

 

CASE 2 (Rewards Credit Card)

Case 2

 

As you can see, FOUR AND A HALF YEARS of a person’s life are saved just by upping their savings rates by a small fraction!

The readers of this blog; however, are decidedly better than the average American, you wouldn’t be reading a blog that talks finance or efficiency if you weren’t. So I’ve also included a table were you can look up how long until you are financially independent.

FI Tables

I made a spreadsheet to do all of these calculations.  I have made it available as a download from my Dropbox.  For those of you who want to tinker with my assumptions please go for it. Spreadsheet

If you have any questions about how I came to these conclusions please let me know in the comments.

 

2 thoughts on “Why 2% is Such a Big Number”

  1. Matt this is fantastic! Good work man. Definitely going to tinker with the spreadsheet. Now I just need to figure out what my true savings rate actually is and my investment rate. Can investment rates be anything (house appreciation, stock returns, 401k etc.)?

    1. Hi Jace, Yes, investment rate or your compounding rate comes from any asset. Stocks, bonds, interest bearing accounts, real estate rentals, and ownership of a business are all good examples. Be careful when counting your primary residence though. The purpose of this compounding is to use for everyday expenses and the equity in your house is hard to access. Now if you plan to sell your house in the future and buy something smaller then go ahead and include that in your compounding rate.

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