Today, we're going back to basics to look at the core mechanics of saving and investing—how it actually works, and how to make it work for you.
Quick agenda:
About me
How long will it take for my money to double?
Compound Interest, often called the Eighth Wonder of the World.
Regular Savings and Compound Interest: how I was able to retire early.
Inflation is also a form of Compound Interest, and not in a good way.
TL/DR (aka Summary)
About me
After 25 years in high-tech CPU design and an early retirement package at 50, I spent 8 years teaching computer science at a local charter school. When it closed in 2024, I started wondering: Do we actually have enough money to retire? To find out, I went straight to the source and completed the CFP (Certified Financial Planner) coursework. I discovered I loved breaking down complex financial concepts into everyday terms. So, I started this blog to share what I've learned.
How long will it take for my money to double?
It's called the Rule of 72. It’s a super-simple shortcut: divide 72 by your annual interest rate, and the result is roughly how many years it takes for your money to double. If you're earning 7 percent, it takes about 10 years ($72 / 7 is ~10.3, or about 10 years). Simple math, massive insight.
So why am I talking about this if I want to talk about savings / investing / financial planning?
3 reasons:
To avoid inaccurate info, or scams, it helps if you know some basics on how interest works.
If we want to trust tools, we need to have an idea on what the answer looks like, feels like, sounds like.
This really is pretty simple math, and you can do it. If someone is explaining something, and it’s super complicated, can they break it down and explain it to you like you are in the 5th grade. If it involves investing and they cannot, beware. Many, many, many financial products that are scary complex a lot of money for the people who set them up and those who sell them, and almost no one else. Why is that?
Compound Interest, often called the Eighth Wonder of the World.
Let’s switch to the spreadsheet to see how it works (putting a copy of the spreadsheet here as an example table, but click the link and enter other interest rates to see what happens).
| Interest Rate | 7.0% | Rule of 72: | 10.3 |
|---|---|---|---|
| Initial Investment | $10,000 | ||
| Year | Interest earned | Total | >= doubled ??? |
| 1 | $700 | $10,700 | |
| 2 | $749 | $11,449 | |
| 3 | $801 | $12,250 | |
| 4 | $858 | $13,108 | |
| 5 | $918 | $14,026 | |
| 6 | $982 | $15,007 | |
| 7 | $1,051 | $16,058 | |
| 8 | $1,124 | $17,182 | |
| 9 | $1,203 | $18,385 | |
| 10 | $1,287 | $19,672 | |
| 11 | $1,377 | $21,049 | Yes |
| 12 | $1,473 | $22,522 | Yes |
| 13 | $1,577 | $24,098 | Yes |
| 14 | $1,687 | $25,785 | Yes |
| 15 | $1,805 | $27,590 | Yes |
Regular Savings and Compound Interest: how I was able to retire early.
What happens if we add in some additional money every year (see the 2nd tab of the same spreadsheet above). Note: I left the “>= doubled ???” column in there, but that approximation doesn’t work in this case, but it does help highlight that the combination of compound interest and year savings is what really speeds things up).
| Interest Rate | 7.0% | Rule of 72: | 10.3 |
|---|---|---|---|
| Initial Investment | $10,000 | ||
| Yearly Save additional | $1,000 | ||
| Year | Interest earned | Total | >= doubled ??? |
| 1 | $700 | $11,700 | |
| 2 | $819 | $13,519 | |
| 3 | $946 | $15,465 | |
| 4 | $1,083 | $17,548 | |
| 5 | $1,228 | $19,776 | |
| 6 | $1,384 | $22,161 | Yes |
| 7 | $1,551 | $24,712 | Yes |
| 8 | $1,730 | $27,442 | Yes |
| 9 | $1,921 | $30,363 | Yes |
| 10 | $2,125 | $33,488 | Yes |
| 11 | $2,344 | $36,832 | Yes |
| 12 | $2,578 | $40,410 | Yes |
| 13 | $2,829 | $44,239 | Yes |
| 14 | $3,097 | $48,336 | Yes |
| 15 | $3,384 | $52,719 | Yes |
Inflation is also a form of Compound Interest, and not in a good way.
You probably know average inflation is around 3%. Why do we care if we’re talking about savings / investing / financial planning? Inflation is the evil twin of compound interest. Think of it as negative interest. If something costs $10.00 today, and inflation is 3%, that means it will cost $10.30 next year. So your $10.00 can’t buy everything it used to, but only $10.00/$10.30 = 0.971, or $9.71 worth of stuff. If we treat inflation as negative interest, so -3%, it’d say next year we’d have $9.70 - almost the same number, so we can use the same spreadsheet with negative values to model interest.
AND, we can do something similar with the Rule of 72, that is, treat a negative result for time as being negative years, but how long before the purchasing power of $10 (or $10,000) gets cut in half (the opposite of doubled). Rule of 72 says 24 years, doing the math in a spreadsheet says it’s just over 22 years:
| Interest Rate | -3.0% | Rule of 72: | -24.0 |
|---|---|---|---|
| Initial Investment | $10,000 | ||
| Year | Interest earned | Total | >= doubled ??? |
| 1 | -$300 | $9,700 | |
| 2 | -$291 | $9,409 | |
| 3 | -$282 | $9,127 | |
| 4 | -$274 | $8,853 | |
| 5 | -$266 | $8,587 | |
| 6 | -$258 | $8,330 | |
| 7 | -$250 | $8,080 | |
| 8 | -$242 | $7,837 | |
| 9 | -$235 | $7,602 | |
| 10 | -$228 | $7,374 | |
| 11 | -$221 | $7,153 | |
| 12 | -$215 | $6,938 | |
| 13 | -$208 | $6,730 | |
| 14 | -$202 | $6,528 | |
| 15 | -$196 | $6,333 | |
| 16 | -$190 | $6,143 | |
| 17 | -$184 | $5,958 | |
| 18 | -$179 | $5,780 | |
| 19 | -$173 | $5,606 | |
| 20 | -$168 | $5,438 | |
| 21 | -$163 | $5,275 | |
| 22 | -$158 | $5,117 | |
| 23 | -$153 | $4,963 | |
| 24 | -$149 | $4,814 | |
| 25 | -$144 | $4,670 |
But why do we say inflation also compounds? If the price is $10, 3% is $0.30. If the price has already risen to $20 (because of inflation), that 3% is now $0.60, so we end up paying inflation on already inflated prices.
And some of you are saying “So?” If you are planning on having $50,000 (in today’s dollars) to spend in 24 years, with inflation, you need about $100,000. Yeah - inflation makes this equation true (approximately):
$100,000 in 2050 dollars = $50,000 in 2026 dollars
Net net: if you’re only earning about 3% on your money, while the total is going up every year, it’s not really growing, in terms of purchasing power, as it’s just keeping up with inflation.
So there’s 2 more tabs in the spreadsheet, where it uses the Real Interest Rate (it discounts future money to today’s dollars by removing the effect of inflation, so they are more understandable / real).
| (Nominal) Interest Rate | 7.0% | Rule of 72: | 10.3 |
|---|---|---|---|
| Initial Investment | $10,000 | Inflation Rate | 3% |
| Real Interest Rate: | 3.9% | ||
| Year | Interest earned | Total | >= doubled ??? |
| 1 | $388 | $10,388 | |
| 2 | $403 | $10,792 | |
| 3 | $419 | $11,211 | |
| 4 | $435 | $11,646 | |
| 5 | $452 | $12,099 | |
| 6 | $470 | $12,568 | |
| 7 | $488 | $13,056 | |
| 8 | $507 | $13,564 | |
| 9 | $527 | $14,090 | |
| 10 | $547 | $14,637 | |
| 11 | $568 | $15,206 | |
| 12 | $591 | $15,796 | |
| 13 | $613 | $16,410 | |
| 14 | $637 | $17,047 | |
| 15 | $662 | $17,709 | |
| 16 | $688 | $18,397 | |
| 17 | $714 | $19,111 | |
| 18 | $742 | $19,854 | |
| 19 | $771 | $20,625 | Yes |
| 20 | $801 | $21,426 | Yes |
So to double our money, taking inflation into account, we do need more time, or a better rate of return.
BTW - we can use the Rule of 72 and take inflation into account, if we quickly approximate the Real Interest Rate by just subtracting inflation from the (nominal) Interest Rate: 7% - 3% = 4%. And the Rule of 72 gives 72 / 4 = 23 years, which is pretty close to the 19 years from the spreadsheet doing the formal yearly calculation for compounding.
Approximations are great for quick mental math, seeing if you’re in the right general direction without having to use something more complex or precise. But, if you want an exact number, you’ll want to use a financial calculator, or spreadsheet, to help you do the precise math!
TL/DR (aka Summary) -
Compound interest is awesome - it makes our money grow faster, because we earn interest on our interest (that’s the compounding).
The Rule of 72 quickly approximates how long it takes to double our money, at a given interest rate..
Inflation also has a compounding effect.
We can use the Rule of 72 for looking at inflation by treating it as a negative interest rate, and then the result is the amount of time for our spending power to get cut in half, or by approximating the Real Interest Rate and using the Rule of 72.
Keep in mind - the Rule of 72 isn’t precise - it’s an approximation. But it quickly lets you do a what-if. If someone says you can double your money in 4 years, you can quickly figure out that’s like earning 18% interest. If that was possible, everyone would already be doing it. Being able to do that in your head in 5 seconds can save you from some costly mistakes!
And now that I’ve said earning 18% interest (or return) is a scam, there are ways to earn 18%, or 25% in a year. With risk. Stocks have great years when they earn more than 18% - I’ve had a stock account since 1997, and I’ve seen the S&P 500 do better or worse than +/- 20% over 10 times since 2000:
-23.7% in 2002 (over -40% down for 2000-2002)
+26.4% in 2003
-38.5% in 2008
+23.5% in 2009
+29.6% in 2013
Anyone who says you just have to buy low and sell high is like saying doing a marathon is just a matter of running a bit. Simple to explain, not as easy to do, which is why Buy & Hold is generally the best advice for everyone.
Stay tuned for more updates.
