# The Power of Compound Interest | Early Paycheck

Hey guys,

I had a thought experiment this week that I waned to try out on compound interest.

To start, I want to set the table on compound interest. If you’re reading this, you may have heard many fun examples illustrating just how ridiculously large compounded interest can be. Large in a way that doesn’t intuitively make sense to us.

My favorite example of the power of compound interest is from an old asian proverb.

The shortened version of the story goes – many hundreds of years ago, the emperor asked a game maker to make him a game. The game maker returns having made the modern day game of chess.

After showing the game to the emperor, he was so impressed with a game-maker’s invention, the emperor offers him a reward. He asks how the game maker would like to be rewarded for his wonderful new invention.

The game-maker, well aware of the power of compound interest works, suggested just one grain of rice for the first square of the board. Then, he suggested receiving double the amount on the second square, equaling two grains of rice. After stopping at the second square, he suggested doing this for the entire board and asked the emperor if he would be willing to do this for the entire 8×8 board.

Seeing the small amount of rice initially requested, the emperor agreed — and from that moment was doomed.

By the sixth row of the 8×8 chess board, the collective weight of the rice owed to the game-maker is equal to the weight of all the modern-day cars than exist on the planet. There are still two more rows to go.

I love this example because it shows how much effect doubling has given enough time. The same principle applies to investments. While investments don’t double every year, even a small rate of return over time adds up to a lot.

So — now to my example from earlier. One of my coworkers was recently talking about how they could receive their paycheck a couple of days earlier than the official posting of pay from your employer. After a quick google search online, it looks like this is a feature is possible at many banks.

I got to thinking. While it seems like such a small thing, I bet receiving your paycheck two days early allows you to make

How much additional money could you make over the course of your life if you received your paycheck two days earlier in the week every single paycheck?

It seems like a silly question. Will getting your paycheck a couple of days early and investing the same amount of money as you would have if you received your normal paycheck really make a difference? I was really curious to see if it did, so I investigated myself.

In order to calculate the impact of getting paid a few days early, I had to make some assumptions and assign some variables. I used median/average numbers as opposed to my personal numbers. It’s safe to assume that this number would be significantly larger

I took the median income and made some pretty conservative investment assumptions. Let’s list out my assumptions and calculations.

Assumptions:

• You get paid Bi-Weekly (26 paychecks per year)
• You earn rate of return on your investment of 7% annually (This equates to an average return of 0.027% per trading day)
• You earn the median personal income for a 20 American individual of \$35,805
• October of 2021 American average savings rate of 7.3%
• Within this 7.3% savings rate, I assumed that one third of this savings would be invested in the market.
• I assume 12% federal taxes and 4% state taxes taken before investment
• (After-Tax Income of \$30,076.20)

These are all of the ingredients we need to do our analysis. I’ll show my math below, so feel free to substitute your numbers to see how much additional money you could make by investing two days early due to an early.

Alright, first, we need to show how much you’ll be earning after tax during the year. We’re going to assume that you make a median income and get taxed at 12% federal and 4% state + local income tax.

Post-tax income: = 35,805 – ((\$35,805) x (.16)) = \$30,076.20

We then need to take this income and determine what percentage of it you’ll be investing. We’re going to use more assumptions here. We’re going to assume that you save at the October 2021 American average savings rate of 7.3%.

Because the savings rate includes money left over after saving and investing, we need to assume a sub-percentage of this savings rate as investing vs. saving. Let’s say that you invest one third of all the extra money you have left over after your expenses. We can now figure out your investing rate

Investing Rate = (.073333)/3 = 0.0241 = 2.41% investing rate

You invest 2.41 percent of your overall post-tax money per year, so let’s calculate that number.

Annual amount invested: .0276 x \$30,076.20 = \$724.54

Alright cool, now let’s determine how much money you invest per paycheck. If you invest \$724.54 per year and receive 26 bi-weekly paychecks, you invest around \$27.87 per bi-weekly paycheck.

Now here comes the fun part. I’m using another assumption here. The assumption is that on average, the stock market will return you 7% annually for the next 40 years. 7% per year, how much is that on average per trading day? We are trying to see how much more you can make by taking advantage of a few days, so each average daily return matters.

There are 253 trading days per year, so if you take the average annual rate of return and divide it by trading days (7%/253) you get an average trading day return of around 0.0276%.

Now obviously the market isn’t going to go up 0.0276% per day forever, but this will be a good way to use an average rate of return assumption.

Next, we combine our numbers together. We’re trying to see how much extra money investing we could earn by receiving our paycheck two days early, and investing our money in the market two days earlier than if we received a normal paycheck.

First, let’s understand how much additional money we would earn

It’s pretty easy to alter this example for your numbers. You just need to adjust your post-tax income and your personal investing rate post-expenses and you can figure out how much it benefits you. Let’s take a look at how much additional money I would earn from this over 40 years.

Using the assumption that we would get paid on Wednesday instead of Friday, we would receive an additional two trading days in the stock market for our money. If our one day average return in the market is about 0.0276%, our two day return would be around 0.055%.

So now, we have a rate of return assumption for our money, as well as the amount we invest on average bi-weekly. If we invest \$27.87 bi-weekly, assuming an average rate of return of 0.055% for that \$28 for investing it in the market two days early, we end up making an extra \$1.54 every other week by investing two days early. Given there are 26 paychecks over the year for bi-weekly pay, we would earn on average an additional \$40.09 per year from getting that paycheck two days early.

That seems like chump change, but we can stretch it out over the course of a working lifetime and see what the advantage is over 40 years.

Now the beauty of compounded interest states that given enough time, all of the extra money we earn early in our working years add up over time.

So when we stretch out the advantage we have over 40 years, it’s not as simple as multiplying that \$40.09 by 40. The reason is because that money is ALSO EARNING 7% annually in addition to the money we will continue to make by investing two days early.

Think of the equation like this. Instead of \$40.06 x 40, we would do ((\$40.09 +(\$40.06 *.07)) + \$40.06. We already have our \$40.09 from year one. That \$40 earns seven percent, so we want to add seven percent of that number to \$40.09. That number comes out to \$2.81. So we would add (\$40.09 + \$2.81) + \$40.09 = \$82.99. By year two, we earn an additional \$82.99 over what we would have if we received our paycheck and invested on a Friday, as opposed to two days earlier every week.

I made an excel formula to stretch this out for 40 years and the results are pretty cool – take a look.

By year 40, you would have earned an additional ~\$8,000 by investing two days early, and by year 45 you would earn an additional ~\$11,500. That’s decent used car, a nice family vacation, or a trip to the world series of poker just by investing your money two days early.

Keep in mind, for this example I used conservative assumptions – i.e. a median individual income, and an average savings rate. Many finance folks like myself who are obsessed with this stuff invest a lot more, so I wanted to see how much additional money I could make from something like this.

I make ~82k per year from my salary, so let’s use that to calculate my potential gain from an early paycheck.

I’m going to use an effective tax rate assumption of 15% for federal taxes and 5% for state + local tax.

My after-tax income in this example would be \$65,600. We know that there are 26 paychecks per year, so we can calculate my post-tax bi-weekly income of \$2,523.08. I invest about 10% of my post-tax income in taxable investments, so I’m going to use that for our example here. In that case, I’d allocate about \$252.31 bi-weekly to these investments.

Let’s use our same “early investing” multiplier of 0.055% gain for two trading days. (0.055 x 252.31) = \$13.96. I make an additional ~14 bucks per pay cycle by investing my money two days early. Let’s take that x 26 paychecks (\$13.96 x 26) = \$262.96. This is the advantage annually that I would receive by investing two days early. Similarly to last time, I’m going to run a compounded example of what this amounts to over time. Before you see the graph, do you have a guess as to what this would be?

Here’s a graph of the results:

By year 40, I would earn an additional \$58,000 over what I would have earned by investing on Fridays. What the actual f*ck. Also, this example assumes that I make \$82,000 every year for the rest of my working career. Realistically, I would expect to have some sort of wage increase over time.

Another way to think about this example is – this is how powerful two days is for an investment every year. All that’s happening is I’m gaining a two day advantage one time per year for 45 years in a row. There’s only two total days of investing advantage per year.

If you liked this post please consider liking it, commenting, or sharing with friends. It took me a bit of work to put this together, but I love to share the power of investing with others, so I hope this example opened some eyes to compound interest.

Until next time, happy investing!