Are you interested in interest? You should be. Matter of fact, it’s the driving force behind your future retirement so you should be VERY interested. So let’s talk about it. Interest is the money your bank pays you when you deposit your money into your savings account. I won’t get into WHY they would want to pay you since they’re the ones providing you with the service of securely storing your money so that it’s accessible to you anywhere they have a branch, but let’s just say they’re not paying you just to be nice. This article is about interest but the logic and math applies to anything that increases or decreases by a constant percentage every year including stocks, bonds, credit card interest, etc. So instead of calling it interest, let’s be more broad and simply call it the “rate of return.”

As usual, I’ve made a Google Spreadsheet for you to follow along with. I highly recommend you copy it, and change the numbers to following along with the discussion. The only cells you need to change are:

- Annual rate of return
- Annual inflation rate

# Case 1: One Deposit with Zero Inflation

First let’s assume there’s no inflation. I’ll get into this a bit later. Let’s also assume we just make 1 deposit of $1,000 during year 1 and leave it there for a long time. A LONG time, like tens of years. Just change the spreadsheet values to:

Annual rate of return | 5% |

Annual inflation rate | 0% |

Here’s what the money looks like by year:

Feel free to run your mouse over the curve to get the specific values. Here’s the balance for a few milestone years:

Year 1 | $1,000 |

Year 10 | $1,551 |

Year 20 | $2,527 |

Year 30 | $4,116 |

In year 1, you start with $1,000 and by year 30 it’s $4,116, that’s 4.1 times of your initial investment. Not too shabby! But take a closer look at the numbers.

## A closer look at the numbers

Notice how the curve above isn’t quite a straight line. Actually, it looks like the side of a rice bowl; i.e. curved. This means your money isn’t just increasing a bit each year, but the amount of increase itself INCREASES. What?!?!

That’s the main idea behind compounding. Each year your money goes up by the rate of return, here assumed to be 5%, but it goes up as the percentage of THAT year’s balance. So in year 1 you have $1,000, then year 2 it’s $1050 because you’ve earned 5% of $1,000 (which equals $50). But then by year 3, you don’t just get another $50, you get another $53. This is because you take the year 2 balance of $1050 and you add 5% of THAT (5% x $1050 = $53). And this “increase of the increase” just keeps happening …forever… or at least until you take out your money. Ever heard the term “the rich get richer?” Yep, they do.

# Case 2: One Deposit with 3% Inflation

Uh oh. What’s inflation? Well, have you noticed how prices of everyday things like milk, gas, and fried rice cost more today than they did 10 years ago? Turns out this is always happening. Prices go up, I think most people believe that. What does this mean for our savings/retirement account? Trouble.

In recent history, the inflation rate in the United States has hovered at around 3%. This means although our money is growing (let’s assume at 5%) prices also go up so really our money is growing at 2% (5% – 3%). When economists correct for inflation by stating things in “today’s dollars,” they call the new results “real.” So while our annual rate of return is 5%, our real annual rate of return, after adjusting for inflation, is 2%. What does this do to our balance year by year? It doesn’t look good:

Turns out, due to inflation, your real balance isn’t growing very fast at all. Suddenly it seems as if we’re better off just spending the $1,000 on a heck of a weekend in Vegas than trying to save for any sort of retirement.

Unless…..

# Case 3: We Forge Ahead Aggressively Despite Inflation

So far it sounds like retirement is just so discouraging that maybe it’s better to just sweep it under the rug and worry about it when the time comes. Probably not the bad idea. I don’t know…I wouldn’t get on a train if the engineer told me he’s not sure if the tracks last the whole journey. I’d at least want him to show me a schedule of how they’ll be built according by the time we arrive. That is, train engineers and retirees should both have a PLAN.

So how’s this sound? What if, because of inflation, we need a higher rate of return than 5%. What if we go to the bank and say “whats the best you can offer?” and they tell us their interest rate for savings accounts as of 2017 is merely 0.9%? And what if, because we’re talking about retirement years from now, we’re willing to take on more short term risk in order to achieve that higher rate of return? Well, lucky for us in this fantastic country and world we live in, there is a thing called the stock market. Even better, there’s now enough data to show that there’s a very simple way to get most of the returns on the stock market without knowing much at all: S&P 500 index funds (I recommend Vanguard). In fact, none other than Mr. Warren Buffet has stated multiple times that the average person should do nothing more than invest in index funds rather than fantasize about picking the next Apple stock. Investing in the S&P 500 index funds give you a good chance of getting a 10% annual rate of return and thus a 7% real annual rate of return after adjust for inflation.

So what about that plan? Oh yeah. Here’s my proposal:

- Instead of a 1 time investment of $1,000 let’s invest $1,000 each year for the next 30 years
- Instead of worrying about how the market goes up and down every year, since we’re talking a 30 year horizon let’s assume the annual real rate of return is 7%
- Instead of worrying about the market being too high or too low, we instead just stick to our plan through thick and thin. This is called dollar cost averaging. Some years, we buy too high and other too low but in the long term we got a fair “average” price.

Sounds like a pretty aggressive plan. Risky? Somewhat. But I’d say the bigger risk and trying to outpace inflation with a savings account. Even bond yields are only 2%-3% these days. Let’s just put together a spreadsheet with these assumptions and see what happens. Hopefully you’ve downloaded or copied the spreadsheet and played around with some numbers.

Score! According to the plan above, we can achieve a retirement balance of $94,461 after 30 years. Keep in mind this is just with saving $1,000 per year. What if you figured out that you can live frugally and save $10,000 a year? Then you’d end up with 10X as much. Almost a million!

# So What Next?

One plan does not fit all. This is just to open your eyes and the basics of saving for retirement and using spreadsheets so you can better understand the simple math behind it all. Other considerations are vast and include:

- Should I put all my money in stocks? What mixture of stocks, bonds, and cash should I keep?
- What if I want to retire before 30 years from now?
- What if I can’t even scrape together $1,000 a year due to debt?
- Student loans, credit cards, mortgages etc.

These are all hard questions. In the end, like a lot of decisions, it all comes down to mindset and philosophy. You may need to take an even further step back and ask yourself “what makes me happy?” and “what do I want for myself down the road?” Nobody can tell you that. But the good news is there’s a few good resources out there that address these issues. One of my personal favorite is http://www.mrmoneymustache.com. I recommend reading through sites to find your financial footing.