Definition and Examples of Compound Interest
Compound interest is interest earned from the original principal plus accumulated interest. Not only are you earning interest on your beginning deposit, you’re earning interest on the interest.
Think about compound interest a bit like what happens when the "snowball effect" occurs. A snowball starts small, but the more snow that's added, the bigger it gets. As it grows, it becomes bigger at a faster rate.
How Does Compound Interest Work?
To understand compound interest, start with the concept of simple interest: You deposit money, and the bank pays you interest on your deposit.
For example, if you earn 5% annual interest, a deposit of $100 would gain you $5 after a year. What happens the following year? That’s where compounding comes in. You’ll earn interest on your initial deposit, and you’ll earn interest on the interest you just earned.
The interest your money earns the second year will be more than the year before, because your account balance is now $105, not $100.
With compound interest, even if you don't make any additional deposits, your earnings will accelerate.
- Year One: An initial deposit of $100 earns 5% interest, or $5, bringing your balance to $105.
- Year Two: Your $105 earns 5% interest, or $5.25. Your balance is $110.25.
- Year Three: Your balance of $110.25 earns 5% interest, or $5.51. Your balance grows to $115.76.
The above is an example of interest compounded yearly. At many banks, including online banks, interest compounds daily and gets added to your account monthly, so the process moves even more rapidly.
Of course, if you are borrowing money, compounding works against you and in favor of your lender instead. You pay interest on the money you’ve borrowed. The following month, if you haven't paid the amount you owe in full, you will owe interest on the amount you borrowed plus the interest you've accrued.
Compound Interest Formula
You can calculate compound interest in several ways. Learning how to do it yourself can give you valuable insight into how you can reach your savings goals while keeping realistic expectations. Any time you run calculations, examine a few “what-if” scenarios using different numbers and see what would happen if you were to save a little more or earn interest for a few years longer.
A compound interest calculator such as ours makes this calculation an easy one, as it does the math for you, helping you quickly compare investment earnings or borrowing costs.
Some people prefer to look at the numbers in more detail by performing the calculations themselves. You can use a financial calculator that has storage functions for formulas or a regular calculator with a key to calculate exponents.
Use the following formula to calculate compound interest:
To use this calculation, plug in the variables below:
- A: The amount you’ll end up with.
- P: Your initial deposit, known as the principal.
- r: the annual interest rate, written in decimal format.
- n: the number of compounding periods per year (for example, monthly is 12, and weekly is 52).
- t: the amount of time (in years) through which your money compounds.
Doing the Math
You have $1,000 earning 5% compounded monthly. How much will you have after 15 years?
- A = P (1 + [ r / n ]) ^ nt
- A = 1000 (1 + [.05 / 12]) ^ (12 * 15)
- A = 1000 (1.0041666…) ^ (180)
- A = 1000 (2.113703)
- A = 2113.70
After 15 years, you’d have roughly $2,114. Your final number may vary slightly due to rounding. Of that amount, $1,000 represents your initial deposit, while the remaining $1,114 is interest.
A sample spreadsheet on Google Docs shows how it works. There’s also a downloadable copy to use with your own numbers.
Spreadsheets can do the entire calculation for you. To calculate your final balance after compounding, you’ll generally use a future value calculation. Microsoft Excel, Google Sheets, and other software products offer this function, but you’ll need to adjust the numbers a bit.
Using the example above, you can do the calculation with Excel’s future value function:
Enter each of your variables into separate cells. For example, Cell A1 might have “1000,” to represent your initial deposit, and Cell B1 might show “15” to represent 15 years.
The trick to using a spreadsheet for compound interest is to use compounding periods instead of simply thinking in years. For monthly compounding, the periodic interest rate is simply the annual rate divided by 12, because there are 12 months or “periods” during the year. For daily compounding, most organizations use 360 or 365.
In this example, the pmt section has been left out, which would be a periodic addition to the account. If you were adding money to the account monthly, this would come in handy. Type is also not used in this case. You would use this if you wanted to do a calculation based on when payments are due.
Rule of 72
The Rule of 72 is another way to make quick estimates about compound interest. This method can give you a rough estimate of how long it will take to double your money by looking at the interest rate and the length of time you’ll earn that rate. Multiply the number of years by the interest rate. If you get 72, you’ve got a combination of factors that will approximately double your money.
Example 1: You have $1,000 in savings earning 5% APY, or "annual percentage yield." How long will it take until you have $2,000 in your account?
To find the answer, figure out how to get to 72. Since 72 divided by 5 is 14.4, it will take about 14.4 years to double your money.
Example 2: You have $1,000 now, and you’ll need $2,000 in 20 years. What rate must you earn at a minimum to double your money by then?
Again, figure out what it takes to get to 72 using the information you have, which would be the number of years in this case. Since 72 divided by 20 equals 3.6, you’ll need to earn approximately 3.6% APY to reach your goal over that time period.
What It Means for Individual Investors and Savers
As an individual saver and perhaps even investor, there are ways that you can make sure that compounding works out in your favor.
Save Early and Often
When growing your savings, time is your friend. The longer you can leave your money untouched, the more it can grow, because compound interest grows money exponentially over time.
If you deposit $100 per month at 5% interest, compounded monthly for five years, you'll have saved $6,000 in deposits and earned $800.61 in interest. Even if you never make another deposit after that time, after 20 years your account would have earned an additional $7,573.87 in interest — much more than your initial $6,000 in deposits, thanks to compounding.
Check the APY
To compare bank products such as savings accounts and CDs, look at the annual percentage yield. It takes compounding into account and provides a true annual rate. Banks typically publicize the APY since it is higher than the interest rate. You should try to get decent rates on your savings, but it’s probably not worth switching banks for another 0.10% unless you have an extremely large account balance.
Pay off Debts Quickly, and Pay Extra When You Can
Paying only the minimum on your credit cards will cost you dearly. You’ll barely make a dent in the interest charges, and your balance could actually grow. If you have student loans, avoid capitalizing interest charges (adding unpaid interest charges to the balance total), and at least pay the interest as it accrues so you don’t get a nasty surprise after graduation. Even if you’re not required to pay, you’ll do yourself a favor by minimizing your lifetime interest costs.
Keep Borrowing Rates Low
In addition to affecting your monthly payment, the interest rates on your loans determine how quickly your debt will grow and the time it will take to pay it off. It’s difficult to contend with double-digit rates, which most credit cards have. See whether it makes sense to consolidate debts and lower your interest rates while you pay off debt; it could speed up the process and save you money.
What Makes Compound Interest Powerful?
Compounding happens when interest is paid repeatedly. The first one or two cycles are not especially impressive, but the power of compound interest starts to pick up after you add interest over and over again.
The frequency of compounding matters. More frequent compounding periods—daily, for example—have more dramatic results. When opening a savings account, look for accounts that compound daily. You might only see interest payments added to your account monthly, but calculations can still be done daily. Some accounts only calculate interest monthly or annually.
Compounding is more dramatic over long periods. Again, you’ve got a higher number of calculations or “credits” to the account when money is left alone to grow.
The interest rate is also an important factor in your account balance over time. Higher rates mean an account will grow more rapidly, but compound interest can overcome a lower rate. Especially over long periods, an account compounding at a lower rate can end up with a higher balance than an account using a simple calculation. Do the math to figure out whether that will happen, and locate the break-even point.
Withdrawals and deposits can also affect your account balance. Letting your money grow or regularly adding new deposits to your account will work best. If you withdraw your earnings, you dampen the effect of compounding.
The amount of money you start with does not affect compounding. Whether you start with $100 or $1 million, compounding works the same way. The results seem bigger when you start with a large deposit, but you aren’t penalized for starting small or keeping accounts separate. It’s best to focus on percentages and time when planning for your future: What rate will you earn, and for how long? The dollars are just a result of your rate and timeframe.
- With compound interest, you earn interest on interest
- At many banks, interest compounds daily, allowing you
to grow your money more quickly.
- Online calculators make it easy to figure out compound interest.
- Save early to maximize gains.