The Power of Compounding – How Compound Interest Works
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Using compound interest to save and pay for some of life’s goals — college, retirement, car, home, or just a vacation — is a smart way to have your money work for you.
Compound interest is interest that’s added to the principal amount, and then the interest applies to the larger principal as it grows. It’s earning interest on interest, allowing you to see bigger growth of savings and investments over time. If you’re borrowing money, such as through a credit card or home loan, compound interest could cause you to pay more in interest.
In explaining how compound interest works, our focus will be on how you can benefit from it. A way to build wealth with compound interest is to start saving for retirement and other goals when you’re young, because a longer time period increases its benefits. More time allows compound interest to do its job.
In this article
What compound interest is
What is compound interest? Compound interest is basically earning interest on your interest. You also earn interest on the principal amount. But even without adding to the principal, the account balance will grow as interest is paid and then more interest is paid on the higher total.
Compound interest allows savings and investments in your retirement fund, savings account, or other account to grow exponentially. The longer the money sits, the more it grows.
Compounding adds interest earned back to the principal sum so that interest is gained on that already-accumulated interest during the next compounding period.
It’s growth upon growth.
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An example
Suppose you deposit $1,000 in a high-yield savings account that pays a 10% interest rate that’s compounded annually. At the end of the first year you’ll have $1,100. That’s from the initial $1,000 principal and $100 in interest that’s called “simple interest” because it’s based only on the principal amount invested.
At the end of the second year, you’ll have $1,210. That’s $1,100 from the previous year, plus $110 in added interest (10% of $1,100).
Compounding is used to calculate the interest on the original principal and any previous interest earned on that principal.
Your money grows, or compounds, without adding more of your own money to the principal for the initial investment.
Related: Best High-Yield Savings Accounts
The mathematical formula for compound interest
Compound interest is a mathematical formula that we won’t go into extreme detail on but will cover the basics. Here’s the formula:
A = P(1+r/n)nt
- A: Total amount you’ll have at the end of the timeframe
- P: Principal (starting amount)
- r: Annual interest rate, written as a decimal
- n: Number of times the interest compounds per unit of time
- t: Time (often years, but can be daily, weekly, monthly, quarterly, etc.)
You don’t have to do this math yourself. There are plenty of online compound interest calculators. An online calculator run by the U.S. Securities and Exchange Commission allows for monthly contributions or a negative number if you plan to withdraw money every month.
Determining how much money you’ll start with, P, and timeframe (t), is easy. Finding the other two variables of the interest rate, or r, and compounding frequency (n), can take a little more work. Your bank or wherever you’re putting a sum of money should be able to provide this information.
The FDIC tracks national interest rates each month. As of mid-January 2022, the average interest rate on a savings account was 0.06%, which is what it has been for a few years. With interest compounded annually, a $1,000 deposit that you didn’t add more money to would leave you with a profit of $3 after five years at 0.06% interest.
Higher interest rates can help increase that profit, but so can more time.
A 60-month certificate of deposit, which is the longest-term deposit product that the FDIC tracks, pays 0.28% interest, which is about half of what it was two years ago. Compounded annually, $1,000 deposited in such an account for 60 months, which is five years, grows to $1,014.08 for a profit of $14.08.
Why the frequency of compounding is important
Finding a higher interest rate on a savings account is an obvious way to take advantage of compound interest. A potentially bigger factor is the frequency of compounding.
The more often interest is compounded, such as daily instead of once a year, the more your total amount can grow.
Below is an example of how changing the compounding frequency can affect the total amount, even if the interest rate stays the same. The more often interest compounds, the faster your money can grow. Longer compounding periods also help.
Instead of focusing on the currently low rates of savings accounts, let’s go back to our first example of an initial $1,000 paying 10% interest, without any added monthly contributions:
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- Earn up to 4.20% APY
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- Do it all in one app.
- Up to $2M of additional FDIC insurance through a network of participating banks.
Compounding frequency of $1,000 at 10% interest
Compounds daily | Compounds monthly | Compounds annually | |
After 1 year | $1,105.16 | $1,104.71 | $1,100 |
After 2 years | $1221.37 | $1,220.39 | $1,210 |
After 5 years | $1,648.61 | $1,645.31 | $1,610.51 |
After 10 years | $2,717.91 | $2,707.04 | $2,593.74 |
The Rule of 72
Banks use a simple “Rule of 72” formula to quickly determine how fast money can be doubled with compound interest.
The concept is you divide 72 by the interest rate your deposit is earning. Let’s say it’s 3%. Divide 72 by 3, which gives you 24. Your initial investment will take 24 years to double at 3% interest.
Another way to think about it is what interest rate do you need to lock down today to reach a savings goal of $20,000 in 10 years to take a trip around the world?
Divide 72 by 10 years, which equals 7.2. That means you’ll need to earn approximately 7.2% APY, or annual percentage yield. And since we already know that the Rule of 72 is about doubling your money, then your initial deposit must be $10,000 so that it can double at 7.2% interest in 10 years.
Both of these examples require long-term planning. Ten years may not seem so long, though it may to plan a trip around the world. And 24 years to double your money at 3% interest can seem like a long time, though in the world of retirement planning, it’s not so long if you’re looking to retire in 20, 30, or 40 years.
Using the advantage of compound interest
There are many advantages to making the power of compounding work for you. Here are some to be aware of.
Start compounding in your 20s
You’ve probably heard too many times how important it is to start saving for retirement at an early age. Your 20s, preferably.
It’s true, and it may be a message you’re tired of hearing. Who can afford to put away $300 per month when you’re living paycheck-to-paycheck on your first job?
If you can find a side gig to come up with an extra $300 per month, it can go far, thanks to compound interest.
Calculations by The Motley Fool show that to save $1 million by age 65, and earn an 8% annual rate of return on investments, someone who starts saving at age 25 will need to contribute $350 each month to a savings plan to have $1 million saved by age 65.
Pay off debts
Compounding can work against you if you’re financing debt. Many credit cards compound interest on daily balances. You can save money by paying off credit cards in full each month and not carrying balances from month to month.
Some loans such as federal student loans and mortgages usually don’t charge daily compounding interest. If your monthly payment covers the accrued interest, the interest doesn’t compound.
Whenever you’re applying for a loan, check how interest accumulates and when, if ever, it compounds.
Seek daily compounding
A good personal finance tip for building wealth is to look for a savings or bank account that compounds interest payments daily. As shown in the graph on compounding frequency, daily compounding pays off much better than annually, especially after the first year.
Better banking is here.
- No account fees
- Earn up to 4.20% APY
- Up to 2-day-early-paycheck
- No-fee Overdraft Coverage.
- Do it all in one app.
- Up to $2M of additional FDIC insurance through a network of participating banks.
Costs
Knowing how compound interest works and how it can help your principal amount grow may be all the incentive you need to start a retirement plan or savings goal for something else down the road. But before putting your money in an account with a high rate of return, investigate what the costs are immediately and over a number of years.
They can include fees from brokerages for managing mutual funds or stocks, bank fees for opening a savings account, or early withdrawal fees for cashing in a CD early. Factor these costs, which can be annual, monthly, or per use, into the profit you expect to make.
Some financial institutions eliminate certain fees if you have other accounts with them. Many banks, for instance, will waive a monthly savings account fee of $25 or so if you keep at least $250 in the account.
Pros & cons of compound interest
Pros
- Knowing how compound interest works and how to use the compound interest formula can help you determine how long it will take to save for a goal and what interest rate you’ll need.
- Saving early is especially fruitful with compound interest because it helps your money grow faster with a more extended period.
- Even if you don’t add to your initial investment, compounding has a snowball effect on your savings.
Cons
- Compounding can work against you if you have debt, especially with credit cards that daily compound interest charges. Pay off such debts as soon as you can.
- If you’re saving for retirement, compounding still works, but it can make reaching your goal harder. It may require higher monthly deposits to reach a goal.
- Bank fees and other fees can eat into the profits of compounding.
Better banking is here.
- No account fees
- Earn up to 4.20% APY
- Up to 2-day-early-paycheck
- No-fee Overdraft Coverage.
- Do it all in one app.
- Up to $2M of additional FDIC insurance through a network of participating banks.
The bottom line
By doing a little math or using a compound interest calculator, you can quickly see how compound interest can work in your favor.
Even a low initial investment can grow into a healthy bank account if you add to it monthly and let compound interest do its job. A high interest rate helps a lot, but a long time period and letting your money stay there without making withdrawals can help a lot too.
Understanding how compound interest works can show you how time works to your advantage, encouraging you to save early and often. That’s a lesson not enough people learn and follow.
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Writer
Aaron Crowe is a freelance journalist who specializes in personal finance writing and editing. He has worked at newspapers, where he won a Pulitzer Prize, and has written for numerous online publications. These include AOL, US News & World Report, WiseBread, Bankrate, AARP, and many websites focusing on housing, credit and insurance. He lives in California with his wife and daughter.
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