Compound interest

What is compound interest? | The bank rate

Compound interest is a powerful force for consumers looking to grow their savings. Knowing how it works and how often your bank compounds interest can help you make smarter decisions about where to put your money.

Definition of Compound Interest

Simply put, compound interest is the interest you earn on interest. With a savings account that generates compound interest, you earn interest on the initial principal plus the interest that accumulates over time.

When you add money to a savings account or similar account, you receive interest based on the amount you deposited. For example, if you deposit $1,000 into an account that earns 1% annual interest, you will earn $10 in interest after one year.

With compound interest, in year two you’ll earn 1% on $1,010 – principal plus interest, or $10.10 in interest payments for the year. Compound interest accelerates your interest income, allowing your savings to grow faster. Over time, you’ll earn interest on ever-increasing account balances that have grown from interest earned in previous years. Over the long term, compound interest can quickly snowball your interest income and help you build wealth.

Many savings and money market accounts, as well as investments, pay interest. As a saver or investor, you receive interest payments on a set schedule: daily, monthly, quarterly or annually. A basic savings account, for example, can earn interest daily, weekly, or monthly. And compounding means you will receive interest on the interest you have already earned.

How does compound interest work?

The timing of compound interest and interest payment may differ. For example, a savings account may pay interest monthly, but compound daily. Each day, the bank will calculate your interest income based on the balance in the account, plus any interest you have earned that it has not yet paid.

The higher an account’s interest rate and the more frequent compounding, the more interest you’ll earn over time. The compound interest formula is:

Initial balance × (1 + (interest rate / number of compounds per period) number of compositions per period multiplied by the number of periods

To see how the formula works, consider this example:.

You have $100,000 each in two savings accounts, each paying 2% interest. One account compounds interest annually while the other compound interest daily. You wait a year and withdraw your money from both accounts.

From the first account, which only accrues interest once a year, you will receive:

$100,000 × (1 + (0.02 / 1)1×1 = $102,000

From the second account, which compounds the interest each day, you will receive:

$100,000 × (1 + (0.02 / 365)365×1 = $102,020.08

Since the interest you earn each day in the second example also earns interest on subsequent days, you earn an additional $20.08 over the account that compounds the interest annually.

In the long term, the impact of compound interest becomes greater because you earn interest on larger account balances resulting from years of interest earned on prior interest income. If you left your money in the account for 30 years, for example, the ending balances would look like this.

For the annual capitalization:

$100,000 × (1 + (0.02 / 1)1×30 = $181,136.16

For the daily composition:

$100,000 × (1 + (0.02 / 365)365×30 = $182,208.88

Over the 30 year period, compound interest has done all the work for you. That initial deposit of $100,000 nearly doubled. Depending on how often your money was accumulating, your account balance grew to over $181,000 or $182,000. And daily compounding brought you an additional $1,072.72, or more than $35 per year.

The interest rate you earn on your money also has a major impact on the power of compounding. If the savings account paid 5% per year instead of 2%, the ending balances would look like:

1 year 30 years
Annual composition $105,000 $432,194.24
Daily composition $105,126.75 $448,122.87

The higher the interest rate, the greater the difference between ending balances based on compounding frequency.

Bankrate’s Compound Interest Calculator can help you calculate how much interest you’ll earn on different accounts.

How to take advantage of compound interest

There are several ways consumers can take advantage of compound interest.

1. Save early

The power of compound interest comes from time. The longer you leave your money in a savings account or invested in the market, the more interest it can earn. The longer your money stays in the account, the more compounding can occur, which means you earn additional interest on the interest earned.

Take the example of someone who saves $10,000 a year for 10 years and then stops saving, versus someone who saves $2,500 a year for 40 years. Assuming both savers earn annual returns of 7%, compounded daily, here’s how much they’ll have after 40 years.

$1,388,623 $612,116
Saves $10,000 a year for 10 years, then nothing for 30 years Saves $2,500 per year for 40 years

Both people save the same overall amount of $100,000, but the person who saved earlier ends up with a lot more by the end of 40. Even someone who saves $200,000, or twice as much over the full 40 years, ends up with less – $1,224,232 – because less was saved to begin with.

2. Check the APY

The higher an account’s interest rate, the more interest you’ll earn on the money you put in an account and the more compound interest you’ll earn. While the simple interest rate is a good metric to use, the annual percentage yield (APY) is a better metric to look at.

APY shows the effective interest rate of an account, including all compound interest. If you put $1,000 in an account that pays 1% interest per year, you could end up with more than $1,010 in the account after a year if the interest accrues more frequently than once a year.

Comparing the APY rather than the interest rate of two accounts will show who is really paying more interest.

3. Check Dialing Frequency

When comparing accounts, don’t just look at APY. Also consider the frequency of interest of each compound. The more often the interest is compounded, the better. When comparing two accounts with the same interest rate, the one with more frequent compounding may have a higher yield, meaning it may pay more interest on the same account balance.

TJ Porter contributed to a previous version of this article.

Learn more: