How Compound Interest Works and How to Calculate It
The Formula for Making Your Account Grow
Compound interest is one of the most important concepts to understand when managing your finances. It can help you earn a higher return on your savings and investments, but it can also work against you when you're paying interest on a loan.
What Is Compound Interest?
Compounding is a process of growing. If you’re familiar with the “snowball effect,” you already know how something can build upon itself. Compound interest is interest earned on money that was previously earned as interest. This cycle leads to increasing interest and account balances at an increasing rate, sometimes known as exponential growth.
How Does It Work?
To understand compound interest, first, start with the concept of simple interest: you deposit money, and the bank pays you interest on your deposit.
For example, if you earn a 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.
Therefore the interest you earn the second year will be more than the year before because your account balance is now $105, not $100. So even though you didn’t make any 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 now $110.25.
- Year Three: Your balance of $110.25 earns 5% interest, or $5.51; your balance is now $115.76.
The above is an example of interest compounded yearly; at many banks, especially online banks, interest compounds daily and gets added to your account monthly, so the process moves even faster.
Of course, as you can imagine, if you’re 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, you owe interest on the amount you borrowed plus the interest you accrued.
Take Advantage of Compound Interest
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 greater it can grow, because compound interest grows exponentially over time. If you save $100 a month at 5% interest (compounded annually) for 5 years, you'll have made $6,100 in deposits, and earned $836.63 in interest. Even if you never made another deposit after that time, after 20 years your account would have earned an additional $7,484.13 in interest—more than your initial $6,100 in deposits, thanks to compounding.
Check the APY: To compare bank products such as savings accounts and CDs, look at the annual percentage yield (APY). It takes compounding into account and provides a true annual rate. Fortunately, it’s easy to find because banks typically publicize the APY since it’s higher than the interest rate. You should try to get decent rates on your savings, but it’s probably not worth switching banks for an extra 0.10% unless you have an extremely large account balance.
Pay off debts quickly and pay extra when you can: Paying the minimum on your credit cards will cost you dearly because 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 grows, and the time it takes to pay it off. It's difficult to contend with double-digit rates, which most credit cards have. See if 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 things start to pick up after you add interest over and over again.
Frequency: 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.
Time: 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.
Interest rate: The interest rate is also an important factor in your account balance over time. Higher rates mean an account will grow faster. But compound interest can overcome a higher rate. Especially over long periods, an account with compounding but a lower rate can end up with a higher balance than an account using a simple calculation. Do the math to figure out if that will happen, and locate the breakeven point.
Deposits: Withdrawals and deposits can also affect your account balance. Letting your money grow or regularly adding new deposits to your account works best. If you withdraw your earnings, you dampen the effect of compounding.
Starting amount: 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 earnings 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.
The Compound Interest Formula
You can calculate compound interest in several ways to gain insight into how you can reach your goals and help you keep realistic expectations. Any time you run calculations, examine a few “what-if” scenarios using different numbers and see what would happen if you save a little more or earn interest for a few years longer.
Online calculators work the best, as they do the math for you and can easily create charts and year-by-year tables. But many 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 especially for formulas or a regular calculator, as long as it has a key to calculate exponents.
Use the following formula to calculate compound interest:
A = P (1 + [ r / n ]) ^ nt
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) that your money compounds
Example: 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 (1.00417) ^ (180)
- A = 1000 (2.11497)
- 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 along with a download copy to use your 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 and then refer to those cells so that you don’t have to get everything right in one shot. For example, Cell A1 might have “1000,” Cell B1 might show “15,” and so on.
The trick to using a spreadsheet for compound interest is using 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.
- =FV([.05/12],[15*12], ,1000,)
Notice that you can leave out the pmt section, which would be a periodic addition to the account. If you were adding money monthly, this might come in handy. Type is also not used in this case.
Rule of 72
The Rule of 72 is another way to make estimates about compound interest quickly. This rule of thumb tells you what it takes to double your money, looking at the rate you earn 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 exactly double your money.
Example 1: You have $1,000 in savings earning 5% APY. 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 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 to double your money?
Again, figure out what it takes to get to 72 using the information you have (the number of years). Since 72 divided by 20 equals 3.6, you’ll need to earn 3.6% APY to reach your goal.