"Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it." This is a famous quote commonly attributed to Albert Einstein, but fortunately, you don't need to understand the theory of relativity to understand compound interest. And by taking advantage of the power of compounding and having some patience, you can exponentially grow your money.

Put simply, compounding means growth on top of growth. And figuring out compound gains is basically just a math problem, where you calculate percentage changes based on a growing balance.

Suppose you have $100 and it grows by 10%. That means you have a $10 gain, bringing your total to $110. If that new balance of $110 grows by another 10%, you have an $11 gain, since you're working with a slightly larger balance, compared to if you only gained 10% on the original $100.

The difference between $11 and $10 is small, but if you keep going with compounding interest year after year, the effect becomes much more significant over time, especially when working with larger balances.

A similar effect occurs with compound returns, in the context of investment gains from asset price changes.

Suppose you own one share of a stock worth $100. If the stock goes up by 10% one year, the value of your share is now $110. If the stock gains another 10%, that 10% increase of $110 results in an $11 price increase to reach $121.

Some might look at the overall gains, like seeing that the price rose by 21% or $21 total. But compounding is still happening in the sense that the percentage change is based on a growing base number. This effect is important to conceptualize because stock prices are generally about percentage changes, rather than dollar changes.

All things being equal, investors aren't going to treat a $1 stock the same as a $100 stock and bid up the price of both by $1, because that would be saying the $1 stock is now twice as valuable as it was previously, whereas the $100 stock is only 1% more valuable. Instead, if economic conditions supported a 10% gain across stocks, to use a simplified example, then that $1 stock would trade for $1.10 and the $100 stock would trade for $110.

Then, if the same thing happens the next year, it's important to realize that the same performance for what's now a $110 stock would gain $11, not $10 -- not because investors are saying the stock had a better year, but because you're taking the same 10% from a larger base number.

All of this can get a little confusing when trying to do the math in your head, but you can search for a compound interest or compound returns calculator online and see how compounding leads to exponential growth.

However, it's important to understand the slight differences between compound interest and compound returns to maximize your finances. The two terms are similar, but when used in the context of interest income vs. investment returns from asset price changes, there are some nuances that can trip people up.

Here's a closer look at compound interest and compound returns.

Compound interest can have more permanence than compound returns, in the sense that once you earn compound interest, that money is typically yours to keep. Compound returns, however, might just be on-paper returns that you don't end up maintaining.

For example, with compound interest in a high-yield savings account, your balance increases with each interest payout, and unless you withdraw funds, your balance will keep increasing with each interest payout.

With compound returns such as for stocks, however, your balance might increase for a few years, but then a stock market downturn might wipe out some of those gains. If your account doubles from $10,000 to $20,000 after around seven years of approximately 10% annual gains compounded, but then a stock market crash drops your balance by 50% to $10,000, you're back to square one.

That said, compound return averages generally account for these fluctuations. So if you calculate what your balance would look like in retirement if you average 8% returns for 30 years, for example, that could account for some years being far higher than 8% and some years being negative.

Related to compound interest having more permanence, the gains from compound interest are often based on a fixed rate, whereas compound returns are often variable.

For example, compound interest on a certificate of deposit generally involves earning a fixed interest rate on an increasingly higher balance as that interest gets credited to your account, and if you keep your money in that CD for the whole duration, you'll know exactly how much money you'll have at the end. Savings account rates can fluctuate, but you still know what the rate is at a given point in time and typically the changes are slow.

In contrast, you might estimate the average compound returns for stocks or other assets like real estate, but the actual returns are anyone's guess and can be quite volatile.

While the stability of compound interest might lead you to think you're better off sticking money in a savings account than investing, the reality is that compound returns from assets like stocks often yield higher long-term gains than compound interest from savings vehicles or fixed-income assets like bonds.

For example, a high-yield savings account might pay around 5% in a relatively high interest rate environment like we're currently in, whereas the S&P 500 has historically averaged around 10% returns.

So even if you have to deal with some volatility along the way, compound returns from stock market investing, such as within your retirement account, can propel you significantly further than compound interest income, which is typically more modest.