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How Does Compound Interest Work?

April 30, 2024

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Interest is an important concept to understand in personal finance whether we’re talking about saving, investing, or borrowing money.

When you take out a loan, the interest rate reflects the cost of borrowing that sum of money. On the flip side, when you put money into a savings account, interest is what a bank pays you for your deposits. The interest you earn can compound at different frequencies (e.g., daily, monthly, etc.) depending on your bank.

But what exactly is compound interest and how does it work to grow your savings? In basic terms, compound interest is when you earn interest on top of the interest you’ve accrued from your principal. Let’s take a closer look.

Simple interest vs. compound interest

To understand the power of compound interest, it may help to first review how simple interest works.

Simple interest

A savings account that earns simple interest means that your interest earnings will be calculated based only on your principal (original deposit amount). In other words, there’s no compounding effect – you do not earn interest on interest.

Let’s say you open a savings account with an initial deposit of $10,000, and you plan to leave the money untouched for five years. Let’s also assume for illustrative purposes, the account pays you a simple interest at 2.15% APY each year.

For this account, your annual simple interest earnings will be calculated based on your original deposit of $10,000. This means that at the end of every year, you’ll receive $215 ($10,000 x 2.15%) in interest payments.

Starting deposit: $10,000

Year 1: interest earning = $215, account balance = $10,215
Year 2: interest earning = $215, account balance = $10,430
Year 3: interest earning = $215, account balance = $10,645
Year 4: interest earning = $215, account balance = $10,860
Year 5: interest earning = $215, account balance = $11,075

*Example above is for illustrative purposes only; it assumes no withdrawals or additional deposits

So, a $10,000 deposit that’s earning simple interest at a rate of 2.15% over a five-year period would yield $1,075 in total interest earnings.

Good to know: You can calculate simple interest using this formula.

Simple Interest = Principal x Interest Rate x Time

So sticking with our example from above: $10,000 x 2.15% x 5 = $1,075

Compound interest

Compound interest is interest you earn on top of the interest you’ve accrued from your original deposit. Put another way, you’re earning interest based off of your principal balance plus any interest that has been added to your principal over time.

To illustrate this concept of “earning interest on interest”, let’s again use the example from above.

You open a savings account with an initial deposit of $10,000, and you plan to leave the money untouched for five years. Let’s assume for illustrative purposes, the account pays you a 2.15% APY each year – but this time, the interest compounds annually.

In the first year, just like the simple-interest account example above, you would earn $215 in interest ($10,000 x 2.15%), leaving you with the same year-end balance of $10,215.

However, in the second year, you’ll end up with a slightly higher year-end balance vs. the simple-interest account (see calculation table below). Why? Because your interest earning is now calculated based on your new balance of $10,215 instead of $10,000 (the initial deposit).

In other words, you’re earning interest on top of the interest you earned in the first year, which has been added to your principal. The very same 2.15% APY on $10,215 will give you nearly $220 in interest that second year ($10,215 x 2.15%), so you’ll finish that year with a balance of $10,435 rather than $10,430.

Compound Interest

Starting deposit: $10,000

Year 1:

Interest earning = $215
Account balance = $10,215

Year 2:

Interest earning = $220 ($10,215 x 2.15%)
Account balance = $10,435

Simple Interest

Starting deposit: $10,000

Year 1:

Interest earning = $215
Account balance = $10,215

Year 2:

Interest earning = $215 ($10,000 x 2.15%)
Account balance = $10,430

After the five years, you’ll end up with a balance of $11,122, having earned $1,122 total in interest. See the breakdown below.

Principal Balance

APY

Interest Earned (rounded to nearest dollar)

Year-End Balance

	Principal Balance	APY	Interest Earned (rounded to nearest dollar)	Year-End Balance
Year 1	$10,000	2.15%	$215	$10,215
Year 2	$10,215	2.15%	$220	$10,435
Year 3	$10,435	2.15%	$224	$10,659
Year 4	$10,659	2.15%	$229	$10,888
Year 5	$10,888	2.15%	$234	$11,122

*Example is for illustrative purposes only; it assumes no withdrawals or additional deposits

That’s $47 more in total interest earnings when compared to the simple-interest savings account example from earlier ($1,122 - $1,075). While this may not seem like a big difference over the first five years, you can imagine the impact it can have on your savings over the long run – say, in 10, 20, and 30 years. That’s why the earlier you start saving, the better. You’ll be giving your money more time to grow through the power of compounding.

To see the exponential impact of compounding, play around with the simple interest and compound interest calculators that are available online.

One quick note: In our basic compound interest calculation example above, the interest is compounded annually. But keep in mind that compounding can occur at different frequencies – daily, monthly, or annually – as determined by your bank. The important thing to remember is that the more often it compounds, the faster your money could grow.

Good to know: You can calculate compound interest using this formula.

A = ending amount
P = principal
r = interest rate
n = number of times interest is compounded per year
t = time in years

So sticking with our example from above:

$10,000 (1 + 2.15%/1)^(1x5) = $11,122

Compound interest can work for or against you

The power of compounding can impact other parts of your financial life as well – beyond the interest you earn through your savings or investments.

While compound interest can help grow your savings or investments, it can have the opposite effect when it’s applied to credit card balances. As you probably know, unpaid credit card bills can result in interest charges, and credit card interest is typically compounded on a daily basis . That compounding effect could make it harder for you to pay off credit card debt if you let it accumulate over time. That’s why it’s so important to always pay off your balances in full and on time each month.

This article is for informational purposes only and is not a substitute for individualized professional advice. Articles on this website were commissioned and approved by Marcus by Goldman Sachs®, but may not reflect the institutional opinions of The Goldman Sachs Group, Inc., Goldman Sachs Bank USA, Goldman Sachs & Co. LLC or any of their affiliates, subsidiaries or divisions.