What is compound interest? | The bank rate
Compound interest is a powerful force for people who want to build up their savings. That’s why understanding how it works – and how to exploit it – is very important.
Definition of compound interest
When you deposit money into a savings account or similar account, you usually 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 get $ 10 interest after one year.
Compound interest is interest you earn on interest. So in the example above, in the second year, you would earn 1% on $ 1,010, or $ 10.10 in interest payments. Compound interest speeds up your interest income, helping your savings grow faster. Over time, you will earn interest on ever larger account balances that have grown from interest earned in previous years. In the long run, compound interest can snowball your interest income very quickly and help you build wealth.
Many bank accounts, such as savings accounts and money market accounts, as well as investments, pay interest. As a saver or investor, you receive interest payments on a predefined schedule, such as daily, monthly, quarterly, or annually. And the deposits in these accounts will be on top of the interest you earn, paying additional interest on the interest you have already earned.
Depending on the account, interest may be compounded on different time frames. A basic savings account, for example, can earn daily, weekly, or monthly interest.
How does compound interest work?
It is important to note that the timing of compounding interest and paying interest may differ. For example, a savings account might pay interest monthly, but compound it daily. Each day the bank will calculate your interest income based on the account balance plus any interest you earned and did not pay.
The higher an account’s interest rate and the more frequent the compounding, the more interest you will earn over a specified period of time. To illustrate how compounding works, we’ve included the interest compounding formula below, along with a few examples of how compounding affects income.
The compound interest formula is:
Initial balance * (1 + (interest rate / number of compositions per period) ^{number of compositions per period * number of periods}
To see how the formula works, consider this example.
You have $ 100,000 in two different savings accounts, each paying 2% interest. One account compounds interest annually while the other compounds interest daily. You wait a year and withdraw your money from both accounts.
On the first account, which only compounds interest once a year, you will receive:
$ 100,000 * (1 + (.02 / 1)^{1 * 1} = $ 102,000
From the second account, which compounds the interest each day, you will receive:
$ 100,000 * (1 + (.02 / 365)^{365 * 1} = $ 102,020.08
Since the interest you earn each day in the second example also earns interest on the following days, you earn $ 20.08 more than in the account that compounds interest on an annual basis.
In the long run, the impacts of compound interest become larger because you earn interest on larger account balances resulting from years of past interest income. If you’ve left your money in the account for thirty years, for example, the closing balances would look like this.
For the annual composition:
$ 100,000 * (1 + (.02 / 1)^{1 * 30} = $ 181,136.16
For the daily composition:
$ 100,000 * (1 + (.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 dialed, your account balance increased to over $ 181,000 or $ 182,000.
And the daily membership got you $ 1,072.72 more, or over $ 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 closing 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 the closing balances depending on the frequency of compounding.
Our Compound Interest Calculator can help you calculate how much interest you will earn on different accounts.
How to take advantage of compound interest
There are several ways that ordinary people can profit from compound interest.
1. Save early
The power of compound interest comes with time. The longer you leave your money in a savings account or invested in the market, the more interest it will accumulate. 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 people earn 7% annual return, compounded daily, they will have the next amount after 40 years.
Save $ 10,000 per year for 10 years, then nothing for 30 years | Save $ 2,500 per year for 40 years | Save $ 5,000 per year for 40 years |
$ 1,182,470.57 | $ 551,542.64 | $ 1,103,085.27 |
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 their 40s. Even someone who saves $ 200,000, or twice as much in the full 40 years, ends up with less because they are spreading their savings over 40 years instead of making most of their savings up front.
2. Check the APY
The higher the interest rate on an account, the more interest you will earn on the money you put into it and the more compound interest you will earn. While the simple interest rate is a good metric to use, the Annual Percentage Return (APY) is a better metric to look at.
APY shows the effective interest rate of an account, including the entire membership. If you put $ 1,000 into an account that earns 1% interest per year, you could end up with more than $ 1,010 in the account after one year if interest accumulates more than annually.
If the account announces an APY of 1%, you will have exactly $ 1,010 in the account after one year, because APY counts for membership.
Comparing the APY rather than the interest rate of two accounts will show who really pays the most interest.
3. Check the dialing frequency
When comparing accounts, don’t just look at APY. Watch how often they compound the interest. The more often they compose, the better. When you compare two accounts with the same interest rate, the one with the more frequent compounding will have a higher APY, meaning it will pay more interest on the same account balance.
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