Dollar Scholar Asks: What Makes Compound Interest so ‘Magical,’ Anyway?

Even Albert Einstein was a fan.

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“Money” and “magic” are rarely mentioned in the same sentence — unless you’re talking about David Copperfield’s net worth or compound interest.

While I can’t comment on the former, the latter comes up with remarkable frequency in my interviews. In fact, I just searched the phrase “compound interest” on Money’s website, and it makes an appearance in over 230 articles going back to 2012.

Experts particularly like to refer to compound interest as “magic” — legend has it even Albert Einstein was a fan, famously saying “Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.”

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What is compound interest, and what makes it so great?

I got in touch with Julie Guntrip, financial wellness expert at Jenius Bank, to find out. She started with a definition: “Compound interest is when the interest earned on a balance is calculated not only on the original principal amount but also on interest already accrued,” Guntrip writes in an email.

Compound interest lets me earn interest on interest, basically, which can create a snowball that just keeps getting bigger with time.

“It may feel like magic because of this exponential growth potential,” she says. “What starts as a small increase could substantially increase over many years if left untouched, effectively making your money work for you on autopilot.”

Here’s an example. Say I put $1,000 into a deposit account that earns 5% interest annually. After a year, my balance will be $1,050.

But then the next year, I won’t earn another $50 — I’ll earn 5% of that slightly bigger balance, meaning I’ll generate $52.50 and, once it’s added to what I already have, end year 2 with $1,102.50 total. When that happens again in year 3, I’ll have $1,157.63, and so on.

If I leave it all untouched, I’ll end up with $1,628.89 after a decade. After 20 years, my sum will be $2,653.30. And once that account turns 30, the balance will be $4,321.94 — over four times my original investment.

I will have quadrupled my money, and I didn’t even have to do anything.

The numbers are more impressive if I start with a higher initial deposit. After one year, a $50,000 deposit with a 5% interest rate that compounds annually will become $52,500. After 30 years, it’ll be a whopping $216,097.12.

Guntrip says that because time is so crucial here, young people tend to benefit the most from compound interest. The longer a person is able to let their account generate compound interest, the more it expands. That’s why financial experts heavily encourage folks to start saving as soon as they’re able to, even if it’s just a small amount.

I can find compound interest in high-yield savings accounts, certificates of deposit (CDs) and money market accounts. Experian points out that I can also make the most of compound interest by reinvesting earnings from dividend stocks, exchange-traded funds, mutual funds and more.

If you want to nerd out, according to Citi, the formula for calculating compound interest is A = P (1 + r/n)⁽ⁿᵗ⁾. P is the principal, r is the interest rate (as a decimal), t is the period of time, n is how many times interest compounds, and A is what has been earned at the end of the time period.

That math goes over my head, but I don’t have to be Einstein to appreciate compound interest. Guntrip says it’s particularly relevant in retirement accounts like 401(k)s or IRAs, which workers often hold for decades. That’s literal decades of earning interest on a growing balance. The deal is even sweeter if I add to the principal amount over time.

Is “magical” making sense as a descriptor yet?

Unfortunately, compound interest isn’t always a good thing. Though it can vastly increase my savings over time, it can work against me if I’m in debt, Guntrip says.

Credit card interest, for instance, compounds daily, so my amount owed can quickly balloon. Say I have a $10,000 credit card balance with a 20% annual percentage rate, or APR. That 20% divided by 365 days in a year is 0.05479%, so after one day unpaid, my balance rises to $10,005.479. Then the next day, the interest is calculated again using that total, giving me a slightly larger $5.482 in interest (and $10,010.961 in all).

It might seem like fractions of cents are too tiny to be important, but this adds up quickly. By the end of the month, my $10,000 bill will be over $10,151.

“The ‘magic’ becomes a financial burden if payments aren’t managed carefully,” Guntrip adds.

The bottom line

The magic of compound interest lies in the way I’m able to earn interest on a growing balance that just keeps getting bigger over time. Einstein, Benjamin Franklin and Warren Buffett are right: It’s a pretty amazing phenomenon, and one I should take advantage of while I’m young.

My future self will thank me.

More from Money:

When Can Debt Be a Good Thing?

Should I Switch Banks in Pursuit of Better APYs?

How High Can High-Yield Savings Rates Go?