Don’t Put Off Until Tomorrow What You Can Save Today

Okay, round two of the advice column. Deep breath, here we go. I know I promised this would be a “why is having a savings account important” article, but unfortunately, Henry Street has a million ideas and also full-time jobs, so writing every piece that we have sketched out will take a little bit of time. We will once again table that article for a later day. In the interest of transparency, the shortlist of topics we have in mind includes, in no particular order:

• Budgeting
• Monthly savings and how every month everyone should be able to do it
• The importance of an emergency fund
• How much money do you actually need to retire
• Should you be investing while paying off your student loans
• Invest in the market
• Why you should use your credit card for essential purchases
• Why people often behave irrationally when it comes to personal finance

If any of these topics appeal to you, our reader, please feel free to use the Contact page to let us know, and we will see if we can bump it up the priority list. Our thoughts are, that to be informed on saving, you need to know:

1. Why it is important to save/ invest
2. Why it is important to save/ invest now
3. How much you need to save/ invest
4. How to save/ invest/ budget
5. Where you should put your savings/ investments

Last article we focused on one aspect of where to save. This particular topic will not focus on how you can save, nor how much, but rather why you should start ASAP and not deal with retirement savings in five years, or ten. Millennials always think that they have time on their side; they are young and have 40 years until retirement. But time should be working for your money, and it’s the most powerful ally that you have in building your wealth. Everyone knows the adage “a bird in the hand is worth two in the bush.” Well, I want to demonstrate that a dollar today is worth $273 in the future. I give you the magic of compound interest.

To start, for those of you who do not know, Evan and I are modelers by occupation — we make simulations for a living. Does that make us nerds? Undoubtedly. We spend all day Monday-Friday sitting at a computer typing code and utilizing statistics. However, this has taught us the value of making data-based decisions. You’ll notice a trend in our articles; we are very averse to making gut-decisions and very pro letting the data speak for itself. Also, one random housekeeping item: there is a glossary at the end of the article that explains concepts that may not be intuitive; this will help with the flow of the argument.

Using a simple Python script, we created a Monte-Carlo simulation that models what would happen if you invested $100 a month in the stock market each month for a variable amount of time. Our methodology was as follows:

• We found a table (see below) of the performance of the S&P 500 (NYSE: SPY) over the last 30 years
• From that table, we create a normal distribution of SPY performance for any given year
• From the normal distribution, we randomly selected a rate of return and calculated how much money you would have if you started with $0 and invested $1200, or $100 each month, that year
• We then repeated this process forty times, each time assuming that the amount you started the year with was equal to the amount you had at the end of the previous year
• At the end of the forty years, we had an estimated future value of your $48,000 ($1200 a year x 40 years) that you invested
• We then repeated this entire model one million times and looked at the probability of each future value
• Are you still with me? I know this stuff is pretty dense

S&P 500, 30-Year Annual Returns. As you can see, the market is more likely to go up than down, which is indicated by the higher percentage of green than red

Several assumptions go into our model, including:

• SPY performance is normally distributed
• SPY performance is not correlated year-over-year (no bull or bear markets)
• Inflation is not modeled
• Both compounding and deposits are annual, for simplicity’s sake

The following graph displays the results of the model. To understand the chart, you first must know what a Cumulative Density Function (CDF) is. A CDF shows a measurement, in this case, the future value of the investment account, on the x-axis and the likelihood that the measurement will occur on the y-axis. For this CDF, each line represents a different duration over which the investment occurred. Blue corresponds to investing for 20 years, orange for 30, green for 35, and red for 40. The best way to read the plot is thus: follow one of the lines from the top left to the bottom right, and that will tell you the likelihood of your account containing at least a certain amount of money if you invest it for that amount of time. More directly, if you invest $100 every month in the S&P 500, there is a 50% chance that after 20 years you will have $68,000, after 30 years, $187,000 and after 40 years, $480,000. Alternatively, if you want to accumulate $200,000, there is approximately a 3% chance it happens after 20 years, 45% after 30, and 85% after 40.

The most obvious takeaway here is that if you continue to invest for a more extended period, you will have a higher chance to accumulate more in your account. That is intuitive, and I don’t think I needed to build a model for you to understand that. However, the magnitude of the difference is pretty astounding the longer you continue to invest. The exact future account values that are 10%, 50% and 90% likely are summarized in the table below, as well as the total amount of money you will have invested by that time (remember you are depositing $100 each month).

Let’s first examine the 90% likely case, which is as close to a guarantee as you will get. Invest for 20 years, and your expected value is only $12,000 more than the $24,000 you put in. That’s a 50% return on investment (ROI = profits / principal investment). Okay, but not great. What happens if you continue another ten years? Now your expected profits are $45,000, and your ROI is 125%. That’s looking a lot better. What about another ten years, for 40 total? $131,000 in gains and 273% ROI. But hold up a minute, let’s backtrack. Maybe you don’t need to invest for a full forty years; perhaps thirty-five is enough. Looking at the chart, you would expect to have $121,000, which amounts to $79,000 in gains, and an ROI of 188%. And there is the kicker. In the five additional years to go from 35 to 40 years investing, you will contribute an additional $6,000, but your expected profits will increase $58,000, and your expected ROI will increase a whopping 85%!! The magic of compound interest is that the longer you can let your gains compound, the faster your investment will snowball upwards towards the end. In other words, there is a massive difference between starting your retirement savings when you are 25 versus when you are 30.

Human beings are naturally averse to risk, sometimes irrationally so, which will be a topic for another post. Regardless, 90% is pretty likely, what about a more unlikely scenario. In the 50–50 case, after 35 years your investment will grow from $42,000 to $301,000, but after 40 years it will increase from $48,000 to $480,000. That’s almost $180,000 in only five years! All because you got a jump start and invested early! Your return on investment increases from 617% to 900%. And for the dreamers out there that are hoping for 40 years of economic prosperity, you have a 10% chance of making over $1.4M by investing $100 every month (I should point out that due to real-world economic constraints, this is less than 10% likely).

The moral of the story is to get a jump start on your retirement savings if you have not already done so. I know that $50 a month does not seem like much now, but trust me, continue that habit for 40 years and it will add up. The earlier you can start, the more power you are giving time to work its magic for you. And if they hate, then let ’em hate and watch that money pile up — Kanye West

Glossary

• Compound Interest: interest calculated on the initial amount invested, which includes all of the previously accumulated interest; “interest on interest”
• Future Value: the value of an amount of money at some time in the future based on an assumed rate of growth
• Monte Carlo: a simulation that is used to model the probability of different outcomes that are affected by some form of randomness
• Principal: the original amount of money deposited
• Rate of Return / Return on Investment: measures the gain or loss generated on an investment relative to the amount of money invested
• S&P 500: a stock market index that tracks the performance of 500 large U.S. companies. Many consider it one of the best representations of the U.S. stock market. The New York Stock Exchange ticker of the ETF that tracks the S&P 500 is SPY

The Python model is located on my personal GitHub repository; feel free to download and play around with it as you see fit.