# Exponential Growth with the Time Value of Money

My previous post covered the development of a sustainable budget, which is essential for financial stability. But I want to talk about one of my favorite topics: investing.

Like budgeting, investing has a very intimidating reputation that comes with a lot of connotations: betting, risk, financial jargon, market bubbles, market crashes, old retirement accounts, etc. For the most part, as someone on the outside looking in, investing seems like an overly complicated system that is geared to steal you money, or keep your money until you’re too old to enjoy it. I want to assure you that long-term investing is going to be one of the greatest tools to have at your disposal and will have the greatest impact on your financial wellbeing, and I’ll show how you can take prudent decisions forward that could take as little as 10 minutes to set up (along with more detailed options as well for more personal control.)

In these series of posts I’m going to explain the time value of money, tax saving investment accounts, investing strategies, and brokerage options and advising sources.

## The Time Value of Money:

If you’ve ever taken a finance class, you’ve probably remember the term TVM: Time Value of Money. As a refresher, or to introduce this term to those who haven’t heard it before, it is the relationship that money has with the distance in time. There are two fundamental numbers that are identified in TVM calculations and that is Present Value and Future Value, along with the magic number of Interest rate is what determines much of impacts our daily life, from car loans, mortgage rates, bond values, student loan payments, etc. But don’t worry, I’m not going to do a full on Finance course here, but I’ll give a quick example of how this works:

If I gave you two options: receive $1,000 today, or receive $1,500 5 years from now? You also have the option to grow your investment at 10% per year. Before we go and answer this, we’re have to differentiate between Present Value (PV) and Future Value (FV). For option one, the PV is known in that it is worth $1,000 but we don’t currently know what it’s FV is; we don’t know how much $1,000 is worth 5 years from now. Now on the flip side, We know the FV of option B since we know that in 5 years we will receive $1,500, but we don’t know how much that $1,500 is worth today.

If you wait 5 years, you’ll receive 50% more than if you take the money today, but what could you do with that $1,000 today if you invested for 5 years instead? The answer is $1,610.

What this means is that if we can get $1500 5 years from now and we have the capacity to get 10% growth per year, then the present value of $1,500 5 years from now is actually worth only $931.38.

That may be confusing but now let’s look at these options now when we’ve identified the PV & FV of both options:

Option a: PV= $1,000 FV= $1,610

Option b: PV= $931 FV= $1,500

So which would you rather have today: $1,000 today and $1,610 5 years from now? Or $931 today and $1,500 5 years from now? Option a looks more appealing for both today and in the future and thus is the better choice.

This leads to the magical power of compound interest. You would think logically that if you’re getting 10% per year, after 5 years you would be up 50% (10% + 10% + 10% + 10% + 10% = 50%), but that is what is called “simple interest.” Compound interest of 10% looks like this: (1 x 1.10 x 1.10 x 1.10 x 1.10 x 1.10 = 1.61 or 61%).

Here’s my favorite example to show the power of compound interest:

Imagine you had a paper that was infinitely long, so paper quantity in not going to be a limiting factor here, but it’s still a normal sheet of paper. Now imagine if you took that sheet of paper, that is approximately .004 inches thick, and folded it over so now it’s .008 inches thick since it’s now two layers thick at .004 each. But now imagine you folded that sheet over 50 more times, how tall would this paper stand? I’ll give you a few options:

__Option a__: **4 feet*** (the size of a dresser cabinet)*

__Option b__: **20 feet** (*the size of a full grown giraffe*)

__Option c__: **1,450 feet** (__approximately the height of the Empire State Building__).

Ok you know I just talked about the power of compound interest so even though it doesn’t make sense you picked option c since it’s the one that’s pretty absurd to think a stack of papers would be as tall as a skyscraper. Smart thinking, and you would be… wrong.

I cheated because there’s actually an __option d__: **138 million miles** (*distance to the sun*), which is the correct answer. Don’t believe me? You can do the calculation yourself:

(.0039 x 2 x 2 x 2 x 2 x 2 x 2 … (45 more times) ) divided by 12 (to convert from inches to feet) then divide it by 5,280 (to convert from feet to miles) = 138,605,102 miles.

Cool math tricks, but what does this have to do with investing? Well the TVM plays a role in this paper folding trick, since the present value of paper height was .0039 inches, and when the interest rate was 100%, it meant that after 51 periods (typically calculated in years) the future value was 138 million miles. It is an extreme example of showing how important time plays a factor in wealth.

So let’s now look at my second favorite example that is going to be grounded more in reality that I learned from listening to Dave Ramsey: Imagine two people who decided to invest long term for the future, and let’s say on average they were slightly better than the stock market average and gained 12% on average per year.

But one person started at age 19, who she then put in $2,000 per year, but then stopped after age 26 and she never put any more money in, with a total contribution at $16,000. She then let it grow for 39 years until she’s 65.

The second person waited a few years then he started investing at age 27, which then started investing $2,000 per year for 38 years until he was 65 years old. With a total contribution of $74,000.

Who is going to have more wealth at age 65? It is only 9 years difference between starting points and the second person made up for lost time by putting in more than 4 times the amount as the first person.

The answer is the first person, and it’s still not even that close:

First investor at 65: $2,288,996.

Second investor at 65: $1,532,166

The great news is they both ended up doing really well! But the first one put significantly less effort into it, and still ended up with 50% more wealth.

This is why it is so critical for millennials to not wait to start investing long term, every year we wait until we are “ready” severely limits our growth potential. But the flip side is also true: if we can just contribute a little bit now, and be diligent in controlling our finances today, tomorrow doesn’t have to be full of anxiety. We don’t need to worry about if the baby boomers are sucking up all of social security because we won’t even need it!

I want clarify that the scenario was hypothetical, and to average 12% over 40+ years is not easy, but it is a simplified model to show how achievable future financial stability can be.

Now that we understand the importance of the Time Value of Money, we can then move forward into strategies that will safely navigate you towards these kinds of results which I will discuss in detail in my next post.

[…] time from an investment today (if you want better understand this, go back to my blog post on this: https://grantxstorer.com/2018/personal-finance-investing-part-1-time-value-of-money/ […]