# What Is Compound Interest?: Making Your Money Work For You

Eve Chin, VP Deposit Planning & Strategy, First Republic Bank
December 30, 2021

In its simplest form, interest is a fixed or variable percentage added to a principal amount. But many investments or financial accounts use a more complex formula called compound interest, which is applied to both the principal amount and any accumulated interest that was earned.

In other words, compound interest lets you earn interest on interest. On the one hand, you can grow your money if you, say, place your money into a deposit account. And on the other hand, credit card lenders, for instance, can profit from charging interest on the balance of your credit card.

Once you understand how powerful the benefits of compound interest can be, you’ll want to use it to ramp up your investment strategy.

## Compound interest defined

Compound interest is an interest calculation formula that includes both the principal balance and accumulated interest.

Many lending and investing products use compound interest. Unlike simple interest, which is only applied to the principal balance, compound interest includes previously accrued interest, allowing for exponential growth.

### Compound interest vs. simple interest

The main difference between compound and simple interest is as follows:

• Simple interest is accrued on just the original amount.
• Compound interest is accrued on the full balance, which is the principal plus any additional interest that has been accrued.

## How does compound interest work?

You won’t begin to understand the magic of compound interest until the second time that interest is charged to your account. Here’s why: The interest rate is initially applied to just the balance; then the next time interest is applied to the account, it’s done to the balance and the interest that was added the first time. And that compounding will continue moving forward.

Depending on your account terms, compound interest can happen at various frequencies: interest may be compounded annually, monthly, quarterly or daily. As a rule of thumb, the more frequent the compounding, the faster you’ll see interest growth.

For example, the total amount accrued after two years on an investment of \$1,000 that compounds annually at a rate of 3% is \$1,061.83. Here’s how to calculate compound interest:

 Compound Interest Formula The formula for calculating compound interest is as follows: A = P(1 + r/n)nt A = final amount P = initial principal balance r = interest rate n = number of times interest applied per time period t = number of time periods elapsed

Here is that formula in practice using the above example:

P = 1,000 (deposit amount)

r = .030 (the 3% interest rate in decimal form)

n = 365 (days within the time period)

t = 2 (period of time elapsed— in number of years)

Plugging the above information into the formula gives us:

A = 1,000(1 + 0.030/635)(365)(2)

The parenthesis go first.

A = 1,000(1.0004724409)730

Then, the exponents and multiplication go second and third, leaving the account owner with:

A = \$1,061.83

So, investing \$1,000 at an annual rate of return of 3% compounded daily over the span of two years would provide an interest payment of \$61.83, for a total amount of \$1,061.83.

If you change the compounding frequency to annually, the total decreases slightly to \$1,060.90.

## How compound interest can affect your money

Compound interest affects many facets of your personal finances, including as a borrower and as an investor. Have you ever noticed how long it takes to pay down a credit card? One reason may be because when you carry a balance, the compound interest that's tacked on adds up quickly. But if you put money into a savings account or a retirement fund, compound interest will help increase those earnings over time.

The bottom line is that compound interest can work both against you (if you’re paying it) and in your favor (if it’s being paid on your savings or investments).

### Compound interest examples: Saving and investing

Certain types of savings and investment accounts feature compound interest, which can be harnessed to grow wealth.

These include:

• General savings accounts, including high-yield savings accounts
• Money market accounts
• Certificates of deposit
• 401(k) accounts

The presence of compound interest helps you earn money without actively doing anything with that money, aside from keeping it in the account to grow.

### Compound interest examples: Borrowing

While installment loans typically use simple interest, some forms of credit (particularly credit cards) use compounding interest.

Allowing credit card balances to grow can be costly since credit cards typically have high interest rates. Add to that the fact that they charge compound interest — sometimes daily — and you can see why people struggle to get out of debt.

Worth noting is that while mortgages are sometimes cited as using compound interest, that’s rarely the case in the United States. They typically use simple daily interest, which means interest is calculated daily, but only on the unpaid principal. 