- Antonio Buchanan

# "Compound Interest"

"Compound Interest"

**What is Compound Interest**

Compound interest (or compounding interest) is interest calculated on the initial principal and which also includes all of the accumulated interest of previous periods of a deposit or loan. Thought to have originated in 17th century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding such that the higher the number of compounding periods, the greater the compound interest.

**Example of 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.

**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.