“Compound interest is the eighth wonder of the world. He who understands it, earns it... he who doesn’t... pays it.”
This gem of a quote is often misattributed to Albert Einstein (see Snopes and QI) and while the famed physicist probably never actually said it, the sentiment survives for a good reason!
Compound interest has attained almost mythical status in finance because of its almost magical-looking ability to grow money. In this post, we’ll demystify that “magic” to show why compounding interest is truly the key to building wealth. Whether you’re stashing cash in a savings account or investing for retirement, understanding compound interest can change how you think about money.
Let’s dive in!
Compound interest is essentially interest earning on interest. In simpler terms, it means you not only earn interest on the original amount you start with (the principal), but also on the interest that accumulates over time. This is in contrast to simple interest, where interest is calculated only on the original principal and not on any interest gained in prior periods.
In real-world terms, compound interest shows up everywhere. When you deposit money in a bank savings account, the interest you earn can compound if you leave it there. When you invest in bonds or dividend-paying stocks and reinvest the interest or dividends, that’s compounding at work in your investments.
Debt too can compound of course and if you’ve ever carried a credit card balance from month to month, the interest charged (which is a lot) is added to your bill, and then that larger bill incurs interest the next cycle. It’s a case of compounding working against you if you don’t understand it. (see the “Einstein” quote above)
Compound interest works exponentially rather than linearly. This means that over time, growth isn’t just straight-line addition – it’s like a snowball rolling downhill, picking up more snow (interest) as it goes.
The mechanism is simple: each compounding period (be it yearly, monthly, daily, etc.), any interest earned gets added to the principal for the next period’s interest calculation.
Over long periods, this exponential growth can lead to surprisingly large numbers. How much? We can calculate it!
The rule of 72 is a quick mental math shortcut that tells you approximately how long it takes for an investment to double.
The rule says: divide 72 by the annual interest rate (as a whole number) to get the approximate number of years for doubling. For example:
Keep in mind, the Rule of 72 is not an exact formula, just an estimation tool. It works best for moderate interest rates in the range of 6–10%.
Compound interest follows a straightforward formula but if you’re not a “math person,” don’t worry – you can always use a calculator or online tool – but it helps to see what’s happening under the hood.
Online calculators with visualizations:
What we learn in class:
Where:
How to put this in an excel sheet:
| A | B |
| Principal (P in $) | 10,000 |
| Annual Interest Rate (r as %) | 5% |
| Times Compounded Per Year (n) | 12 (monthly) |
| Years (t) | 10 |
| Future Value (A in $) | =B1*(1+B2/B3)^(B3*B4) |
Answer (A) = $16,470.09
That’s how much your $10,000 grows in 10 years at 5% interest compounded monthly!
As for the Rule of 72: 72/5 = 14.4 years, which pretty much lines up.
While compound interest is a powerful tool for growing wealth, it’s important to recognize the quiet force that works against it: inflation. Inflation reduces the real purchasing power of your money over time, which means that the impressive growth you see in nominal terms may not fully translate to increased buying power.
For example, if your investments compound at 5% annually, but inflation is running at 3%, your real return—the amount your wealth actually increases after accounting for rising prices—is only about 2%. Over decades, this difference can add up significantly. Without factoring inflation into your planning, you might overestimate the future value of your investments.
That’s why successful long-term investing doesn’t just focus on maximizing returns—it also considers strategies to outpace inflation. This can include investing in assets with higher expected returns, like equities, real estate, or inflation-protected securities. Additionally, using tax-efficient investment accounts can help preserve more of your gains from being eroded by taxes, further protecting the power of compound interest over time.
“The person who understands it benefits from it!”
While Einstein may not have called compound interest the eighth wonder of the world, the quote still contains a kernel of truth. The real wonder is how small, consistent efforts can lead to massive results over time thanks to compounding.
Your key takeaways are simple:
In the end, the formula for wealth building isn’t a secret at all: save early, invest wisely, reinvest your gains, and give it time.
Compound interest will do the heavy lifting.