What is compound interest?
August 17, 2023 6 min read
Compound interest is a concept that comes up a lot in personal finance—whether it’s related to saving or borrowing.
In general, it’s interest that’s earned or charged on top of existing interest and principal. Compared to simple interest, compound interest is a little more complicated. But knowing how it works can help you better manage your money.
Here are a few basics to get you started.
- Compound interest is interest calculated on both the principal amount and any previous interest.
- Compound interest is different from simple interest, which is only applied to the principal amount.
- Compounding frequency has to do with how often interest is calculated. Depending on the loan or account, interest might be compounded daily, monthly, quarterly or annually.
- Interest that’s compounded more frequently can yield greater returns or larger interest charges over time.
What is compound interest?
According to the Consumer Financial Protection Bureau, “Compound interest is when you earn interest on both the money you’ve saved and the interest you earn.” This compounding effect can help you earn more money and reach your goals faster.
But it can also work in reverse. If compound interest accrues on top of the debt and interest you already owe, you could end up owing more in the long run.
How does compound interest work?
When compound interest is applied to an account you’re adding money to, it can help that money grow even more over time. Here are a few examples:
How compound interest works with savings accounts
Imagine that you invest $1,000 in a new savings account with a 5% annual interest rate. At the end of the first year, you’ll have earned $50 in interest and your total account balance will be $1,050. If you don’t add funds or withdraw money from this account, you’ll earn $52.50 in interest the second year. And your account balance will now be $1,102.50.
Compound interest probably won’t make you wealthy if you never invest more than the principal amount. But consider what could happen if you added an additional $500 per month into your savings over a 10-year period.
With the same $1,000 initial investment and a 5% compounded interest rate, you would have $79,125 in your account within a decade. $61,000 of this balance would come from your principal investment and monthly contributions. And the remaining $18,125 would be earned from compounding interest.
How compound interest works with debt
Compound interest can also be at play on an account or loan you owe money to. So if balances are not paid in full and interest is left unpaid, that interest can compound too and end up increasing over the life of the loan.
Compounding periods also play a role in the amount of interest that accumulates and how it’s calculated. Compounding time frames can be continuous, daily, monthly, quarterly, semiannual, annual or on other regular periods.
In general, the more compounding periods there are, the more compound interest grows. This applies whether you’re earning interest or it’s accumulating on debt.
Simple interest vs. compound interest
Simple interest refers to interest that’s only applied to the principal amount. In other words, it’s interest that doesn’t compound.
You can see the difference in the graph above. Over time, a compounded interest account grows at a faster rate than a simple interest one.
How to calculate compound interest: A formula and example
Calculating your potential compound interest earnings could motivate you to save more money. And it could help you find a savings strategy that works for your financial goals. The Securities and Exchange Commission has a compound interest calculator. You can use it to estimate how much you might earn by putting your money into an account that earns compound interest.
But if you want to do the manual calculations the old-fashioned way, here’s the formula:
A = P(1+r/n)nt
In this formula, the “A” is the total future value of the account. “P” stands for the principal amount invested. The “r” represents the interest rate in decimal form. The “n” is the number of times the interest compounds per compounding period. The “t” represents the total length of time of the investment in years.
So if $1,000 is invested in an account with a 5% annual interest rate for 10 years, the calculation would look like this:
$1,000 x (1 + .05/1)1x10 = $1,628.89
Using that same example, here’s what would happen if the interest compounded daily instead:
$1,000 x (1 + .05/365)365x10 = $1,648.66
The Rule of 72
The Rule of 72 is an easy way to estimate how long it could take an initial investment to double in value with an annual rate of return. To use this formula, simply divide the number 72 by your account’s interest rate.
In the example above, an initial amount of $1,000 was deposited into an account with a 5% annually compounded interest rate. You can divide 72 by 5 to get a value of 14.4 years. That’s about how long it would take the money to double.
Remember, the Rule of 72 is just a rough guess meant to give an idea about how long it takes to grow savings.
Compound interest and credit cards
Compound interest could also come into play if you have a credit card. And it can add to what you owe over time if you do things like carry a balance from month to month.
But one way to avoid interest on purchases is to pay off the statement balance on time each month. Any unpaid portion is carried over into the next billing cycle. This is called a revolving balance. And revolving balances might accrue interest.
It can get a little tricky, but you can read more about how credit card interest is calculated. It’s also important to remember that when you’re looking at the annual percentage rate, or APR, for a credit card, it doesn’t typically include compound interest.
Compound interest in a nutshell
Knowing how compound interest works can help you make informed investment decisions. If you’re working toward personal finance goals, like planning for retirement or building an emergency fund, compound interest might help you along the way. But it’s also important to remember the role compound interest might have when it comes to debt.