# What is the Rule of 72? #illumedati

Hi guys… late post I know.. but I’m going to talk about the Rule of 72 for this Finance Fridays.

This should be a short post about how to estimate how long it will take for an investment to double. There will also be a short commentary on the “first \$1 million is the hardest” and how saving money doesn’t feel rewarding… but it should be.

I’m going to write a few more complicated Finance Friday posts over the next few months. Also, next week on Whatever Wednesdays I’m going to be doing a “Who IS Sensei?” post.

Stock Photo from: Pexels

### Ok, so what is the Rule of 72?

Basically, it’s a simplified way to calculate how long it will take your investment to double given a certain annual rate of return.

Let’s assume your annual rate of return it 6%… which is what I usually use as a “reasonable” estimate:

Divide 72 by 6 and you get: 12 — meaning 12 years.

Now this is just an easier way to do the actual formula which is:

A = P (1 + r/n)^(nt)

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

This formula is obviously a lot more difficult to calculate than the Rule of 72 above, however, it can be simplified if we assume n is 1.

A = P (1 + r/1)^(1t) which is:

A = P (1+r)^t

### Now, how close is the rule to the actual formula?

For \$1 to become \$2, it would take 10.3 years at 7% based on our Rule of 72.

Using the real formula it would be 10.24 years.

So basically, at around the 6-7% return, this is a very reasonable estimate.

### So when would I use the Rule of 72 then?

Remember my post about My Financial Living Will? The Rule of 72 is good way to evaluate a windfall.

For example, if my wife was to receive \$2 million dollars and just threw all of it into a three fund portfolio, how long would it take to double?

Well, if we assume a 6-7% return, then we’re looking at 10-12 years for it to double to \$4 million.

Then another 10-12 years to double to \$8 million… and then 10-12 years for it to double to \$16 million.

So if she received \$2 million and didn’t touch it for 30-36 years until she retired, it would be worth \$16 million.

### Wait… it went from \$2 million to \$4 million in 10 years… but then \$4 million to \$8 million in the following 10 years?

Yup. This is why multimillionaires always say “Making your first million is the hardest.”

If you google that phrase it will return a host of articles explaining “money makes money” and “psychology” behind it. These are both true.

Once you have your \$1 million to your name, you can not add to it at all. As long as you assume 6% interest, it will become \$2 million in 12 years.

Well, imagine if you keep adding to it (and you probably will). Getting to the next \$2 million will come faster than 12 years.

### How much faster?

For example, if you had \$1 million and you kept putting in \$36k a year into it, assuming 6% interest again, you will get to \$1.95 million at 8 years.

You’ve shaved off 4 years by continuing to put away a reasonable amount of money away.

### Ok, what about the psychology of it all?

Well, saving money is hard. There is a reason gambling is addictive. You hit the button, and you either win or don’t. People like winning.

Our brains are setup to love this feedback reward loops. It’s why all these tech companies talk about gamification and giving awards for virtually everything. Even in actual games themselves, you get an achievement for virtually doing anything in the game.

We like to be rewarded.

Unfortunately, the rewards for saving money are both intangible and far off in the future. You don’t “win” anything necessarily, unless you convince yourself that you are “winning”. It requires you to believe in the power of compound interest and index funds.

### So, how do we fix this?

We (you) need to try to rewire our (your) thinking slightly to feel rewarded by saving. This is not easy… and I would venture to say this is even more so for young physicians.

You finished medical school with massive debt and then start making a menial salary as a resident while still paying back your loans. Then you finally start your first “real job”. Unfortunately, you are crushed by the reality of needing to pay back student loans and having zero money in retirement approximately 10 years behind in saving as those your age.

You want some kind of tangible reward for all those years of hard work. And well, saving more money isn’t tangible.

It also doesn’t feel very rewarding to see some numbers in an account, especially when that number is so low. So we need to rewire:

The numbers in the account isn’t your reward. Your reward will be your ability to go to work because you want to, not because you have to.

### What about you? Is it rewarding for you?

I’m actually not sure how or when changed. Here I was 30 years old with extensive subspecialty training but barely any money to my name, and a massive student loan debt to take care of.

I was scared.

I like medicine and my job but I don’t want to do it until I die because I have to. Doing it because I want to is a different story. I want a comfortable retirement… and I had no plan to get there. This was even more disheartening when I looked into the cold hard facts of needing to pay back the massive student loans of both my wife and I. This was compounded by the high cost of living of Hawaii and the exorbitant house prices… Child Care isn’t cheap either.

It won’t be easy, but at least I have a plan now… and it is rewarding to be able to see where I am in terms of my plan.

It’s not real unless you have a plan to execute.

### TL;DR

The Rule of 72 is a simple way to estimate how long it will take for an investment to double if you know the annual rate of return.

For simplicity, the Rule of 72 can be assumed to be 10-12 years if assume 6-7% interest.

The first million is the hardest.

Saving doesn’t feel rewarding… but it should be.

It’s not real unless you have a plan to execute.

-Sensei

Agree? Disagree? Questions, Comments and Suggestions are welcome.