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

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

  • Compound interest takes into account both the principal balance and accumulated interest of an account or loan.
  • Compound interest can earn you more money when applied to savings accounts, but when it comes to loans or other debts, you may end up owing more money.
  • Compound interest differs from simple interest because it includes accumulated interest.

In its simplest form, interest is a fixed or variable percentage added to a principal amount. But many savings 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 — or, it may require you to pay more interest than you would with simple interest. Understanding how compound interest works and how it can affect your money can better prepare you for future investments.

How Does Compound Interest Work?

Compound interest, or compounding interest, takes into account both the principal balance and accumulated interest.

Compound interest can benefit you when you're the investor, but it can also be a hindrance when you're the borrower. As an investor, you’re earning interest on top of the interest you’ve already accumulated, making you more money over the life of your account(s), such as a savings account or certificate of deposit (CD). But when you’re the borrower and have a balance you have to pay back, like with loans and other debts, compounding interest means you’ll have to pay interest on top of the interest you’ve already amassed — so you’ll be paying more the longer you owe. 

Compound interest vs. simple interest

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

The main differences between compound and simple interest are 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?

Compound interest is initially applied only to your principal amount. That sum earns interest over the course of a compounding period, and that interest is then added to your original principal, increasing the amount you have in that account. In the next compounding period, you’ll earn interest on that new larger amount and the cycle continues. This is how compound interest works on savings accounts, but it’s a slightly different process when it comes to loans and other debts

For loans, the previously accrued interest is "capitalized" (or added to the original loan balance) and then interest accrues on top of that. For instance, this happens with student loans when they go into repayment.

Depending on your account terms, and whether you're dealing with a savings account or with debts, compound interest can accrue at various frequencies: interest may be compounded annually, monthly, quarterly or daily..

Compound interest schedule

Different financial institutions will have different compounding interest schedules for the accounts they offer. In general, most savings and money market accounts at banks compound daily. CDs typically compound daily, monthly or semiannually.

Most credit cards compound daily, but if you consistently pay what you owe on the card before it’s due that month, you won’t be charged interest for those periods.

How to calculate compound interest

Compound interest is calculated by multiplying your initial balance by one plus the annual interest rate raised to the power of compounding periods. If you want to find the interest earned, you’d then subtract the initial balance amount from the result.

The formula for compound interest looks like this:

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

For a step-by-step illustration of how this works, let’s look at an example scenario.

Compound interest example

Let’s imagine you deposited a principal amount of $1,000 into an account that earns daily compound interest at an annual interest rate of 3%.

We can take these amounts and plug them into our compound interest formula to calculate the interest over two years. This will give us our interest earned and determine what our total would be.

  • P = 1,000 (deposit amount)
  • r = .030 (the 3% interest rate in decimal form)
  • n = 365 (number of times interest applied per time period)
  • t = 2 (period of time periods elapsed)

Plugging the above information into the formula gives us:

  • A = 1,000(1 + 0.030/365)(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 payout of $61.83, for a total amount of $1,061.83.

How compound interest can affect your money

Compound interest can affect many facets of your personal finances, including as a borrower and as an investor. Depending on the type of investment account you have open, or the type of debt you owe, compound interest will have varying impacts on your finances and goals.

Here are some examples of saving, investing and lending products that use compound interest.

Saving and investing

As previously mentioned, certain types of savings and investment accounts feature compound interest, which can be harnessed to grow wealth.

These include:

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.


Some forms of debt use compound interest, which means you’ll need to pay off more than just the accrued interest on the loan balance.

These include:

  • Credit cards
  • Some personal loans
  • Student loans (in certain situations, e.g., when repayment starts, after a deferment period)
  • Some mortgages (most use simple daily interest)

The longer you have a pending debt, the more interest will compound, costing you more in the long term.

Best ways to take advantage of compound interest

Knowledge of compound interest can help you avoid costly debt and encourage you to grow your wealth.

Here are some strategies to help earn more with compound interest, while owing less:

  • Start saving early: Getting a head start on your savings goals can benefit you in the long run and allow you to better capitalize on compounding interest.
  • Compare annual percentage yields (APYs): Do your research and opt for a savings vehicle that offers competitive rates.
  • Understand compounding schedules: When researching your saving or investment options, look for how frequently accounts compound — the more often the better.
  • Keep the compound interest growing: Avoid premature withdrawals from a compounding account — the longer the money stays in the savings account, the more interest you will earn.
  • Reduce the principal on your debt: Avoid paying more in compound interest by paying off some of the principal amount on your debt each month.

Personal Savings to Help You Meet Your Goals

Start taking advantage of compound interest by checking out First Republic’s Personal Savings options.

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