What is compound interest?

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In a Nutshell

Compound interest is a powerful financial concept that can help make you money or cost you big time, depending on whether you are earning or paying. By understanding how it works, you can help minimize costs while maximizing earning potential.

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Understanding compound interest can help you save money on credit cards and other loans while earning more from savings and investments.

When you sign up for a credit card or student loan, you’ll typically find an interest rate attached to your account. It’s easy to understand that a higher interest rate costs more and a lower interest rate costs less, but if you don’t take compound interest into account, you won’t fully understand the long-term costs of borrowing.

Similarly, when setting up your 401(k) at work or choosing a savings account, compound interest can add up quickly to boost your account balances. It doesn’t matter if you are at the start of your personal finance journey or a veteran at managing your money. Compound interest matters.


Defining compound interest

Compound interest is basically interest on the principal amount plus whatever interest has already accrued.

Breaking it down, we have two factors that add up to make compound interest: interest paid on the principal and interest paid on accrued interest. Principal is the amount borrowed or invested, and interest is a percentage cost or profit based on the principal amount.

In practice, compound interest works by calculating interest on an entire balance, including past interest that’s been added to the balance. To better understand how compound interest works, let’s look at a savings account as an example.

Let’s say you deposit $100 in a savings account that pays 1% interest, compounding annually. At the end of the first year, you would get a $1 interest payment added to your $100 deposit, yielding a $101 balance. If you don’t make any additional deposits, at the end of the next year you would earn 1% on your new $101 balance, so you’d get $1.01 in interest at the 1% rate, a penny more than the previous year, bringing your balance to $102.01. The next year, you will earn interest based on the new, higher balance. This continues as long as the account remains open.

While adding a dollar here and a penny there on a $100 savings account balance does not add up all that quickly, at a higher interest rate and higher balance, the impact is much more dramatic.

Let’s say you have $1,000 saved in an account that pays 10% interest compounding annually. You’d earn $100 the first year and $110 the second year, with the balance growing into the future at the same rate.

Here’s an idea of how compound interest could grow your savings. A balance of $1,000 at a 10% interest rate that compounds annually for 40 years with no additional deposits could grow significantly.

Years Starting balance Ending balance Annual growth

1

$1,000.00 $1,100.00 $100.00

2

$1,100.00 $1,210.00 $110.00

3

$1,210.00 $1,331.00 $121.00

4

$1,331.00 $1,464.10 $133.10

5

$1,464.10 $1,610.51 $146.41

10

$2,357.95 $2,593.74 $235.79

20

$6,115.91 $6,727.50 $611.59

30

$15,863.09 $17,449.40 $1,586.31

40

$41,144.78 $45,259.26 $4,144.48

 

One thing to remember is that there are different compounding schedules. Interest can accrue daily, monthly, yearly or on any other schedule as laid out in your account agreement. A change in the compounding schedule between daily and monthly can lead to an entirely different result. The more often interest compounds, the more total interest accrues over time. This is why it is important to focus on the best interest rates when signing up for a new bank account.

Compounding doesn’t only happen on accounts that make you money. Credit cards, student loans and mortgages can use compound interest to determine how much you end up paying. We’ll look at an example of this in just a minute. 

The math behind compound interest

Now that you know how compound interest works at a high level, let’s take a look at the math behind compound interest so you can better understand how the interest rate and other factors influence the final outcome.

Compound interest formula — you can use this formula to calculate interest by hand or with your favorite spreadsheet program:
A = P(1+r/n)nt

A =

amount after a certain period of time factoring in compound interest

P =

principal amount (the initial amount you borrow or deposit)

r =

annual interest rate (as a decimal)

n =

number of times the interest is compounded per year

t =

number of years the amount is deposited or borrowed

 

While you can bring back your middle-school math skills to solve for interest in any case, it is much easier to use an online compound interest calculator instead of a pencil and paper. We won’t check your work! The Securities and Exchange Commission offers one of the best compound interest calculators around.

If you want to calculate annual compound interest rates in your head on the fly, there is a quick trick you can use to make it easier. Using the Rule of 72, you can estimate how long it would take for an account to double at a given interest rate.

Let’s say you have a retirement account with a $50,000 balance. You estimate you will earn a 9% return (interest rate) on your investment per year. Using the Rule of 72, we just divide the number 72 by the annual interest rate to find out how long it will take to double your balance: 72/9. In this case, you can expect your $50,000 balance to reach $100,000 in about eight years, because 72/9 = 8.

Compound interest and credit cards

We already looked at how compound interest can help you when you’re investing or saving. Now we’re going to look at credit cards to understand how compound interest can cost you.

Credit card issuers often use compound interest to determine what they’ll charge customers for borrowing money. These monthly interest charges are based on your average daily balance and an interest rate that compounds daily (depending on your account’s terms and conditions).

Let’s say you did some holiday shopping in December to the tune of $5,000 on a brand-new credit card, that your card has a 15% APR on purchases compounding daily, and your billing cycle is 30 days.

The first step is to calculate your daily interest rate from your purchase APR. Then you’ll multiply the daily rate by your average daily balance of $5,000. And finally, you’ll multiply the result by days in your billing cycle to end up with that month’s interest charge. Let’s see it in action.

1. Divide the 15% purchase APR by days in a year.

0.15 / 365 = 0.00041096 daily periodic rate

2. Multiply that number by the average daily balance.

0.00041096 x $5,000 = $2.05479452

3. Multiply by the number of days in your billing cycle to get your monthly interest charge.

$2.05479452 x 31 = $63.70

At the start of January, you would have around a $5,063.70 balance. Because of the way interest compounds, if you were to make timely $63.70 payments every month to pay off the interest, and not do anymore spending on the card, the balance would never go up or down. Paying more than your monthly interest would bring the balance down, while paying less than the $63.70 would mean the balance would rise incrementally over time.

This also means that your payments are not making progress toward reducing the principal until the interest is paid. By paying more than your monthly interest charges, you can help lower your balance, which can also lower what you pay in interest.

Also keep in mind that if you pay off a credit card in full every month by the due date instead of carrying a balance, you don’t ever have to pay any interest on your purchases.


Bottom line

Compound interest is a powerful force. It’s rumored that Albert Einstein once said, “Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”

While he may not have actually uttered those words, there is an important truth in there.

Knowing how compound interest works just might be your new super power — you can use it to your advantage to help grow your wealth by saving and investing. On the flipside, not understanding could mean you’ll end up paying a lot of money in interest.

But now that you have a better understanding of how compound interest works, you can get started paying off debt and investing in a way that puts your money to work for you.