How Compound Interest Works and How to Calculate It
How Compound Interest Makes Accounts Grow
Compound interest is one of the most important concepts to understand if you want to manage your finances. It can help you when you save and invest, and it can make things worse when you’re a borrower. In other words, it can work for you or against you.
What is Compound Interest?
Compounding is a process. 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 – which is sometimes known as exponential growth.
Start with the concept of simple interest: you deposit money, and the bank pays you interest on your deposit. For example, you might deposit $100 for one year at 5%, and you’d earn $5 in interest over the year.
What happens next year? That’s where compounding comes in. You’ll start earning interest on your initial deposit and you’ll earn interest on the interest you just earned:
- You’ll earn 5% on your $100 (again)
- You’ll earn 5% on the $5 of earnings that the bank deposited to your account
That means you’ll earn more than $5 next year (because your account balance is now $105 – even though you didn’t make any deposits), so your earnings will accelerate. At many banks, especially online banks, interest is compounded daily and added to your account monthly, so the process moves even faster.
Of course, if you’re borrowing money, compounding works against you. You pay interest on money you’ve borrowed, and your loan balance can increase over time – even if you don’t borrow any more money.
Take Advantage of Compound Interest
How can you make sure that compounding works out in your favor?
Save early and often: when growing your savings, time is your friend.
It takes a while to get momentum, but that momentum will build and eventually gain strength. In some cases, starting early means you don’t need to save as much as somebody who waits to start saving – even if you quit saving at some point, your head start can pay dividends later. Be patient, leave your money alone, and think long-term.
Check the APY: to compare bank products such as savings accounts and CDs, look at the annual percentage yield (APY). This takes compounding into account and provides a true annual rate. Fortunately, it’s easy to find – banks typically publicize the APY because it’s higher than the interest rate. 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 – pay at least 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 how hard it will be to pay it off). Double-digit rates are difficult to contend with. See if it makes sense to consolidate debts and lower your interest rates while you pay off debt.
Limitations: compounding can help you grow your money, but it falls just short of being magical. To take advantage of compounding, you need to actually save money, deposit it into an account, and earn money on your savings. To end up with any meaningful savings, you need to do this over and over – month after month and year after year. Compounding can’t do the heavy lifting for you.
What Makes Compound Interest Powerful?
Compounding happens when interest is calculated 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.
How often: the frequency of compounding is important. More frequent calculations (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.
How long: compounding is more dramatic over longer periods of time. Again, you’ve got a higher number of calculations or “credits” to the account when money is left alone to grow.
Other factors: the interest rate is also an important factor in your account balance over time. Higher rates mean an account will grow faster. But it’s possible for compound interest to overcome a higher rate. Especially over long periods of time, an account with compounding and a lower nominal 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 where the breakeven point is.
Withdrawals and deposits can also affect your account balance, but they are separate from compounding. Letting your money grow (or continually adding to your account) is best – if you withdraw your earnings, you dampen the effect of compounding.
The amount of money does not affect compounding. Whether you start with $100 or $1 million, compounding works the same way, and your account balance looks the same if you chart the growth over time. Obviously, 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 – how much will you earn, and for how long? The dollars are just a result of your rate and timeframe.
Frequent compounding (daily or monthly) is helpful, but don’t get confused by the numbers. When interest is compounded daily, you still earn more or less the same APY. For example, an account paying 5% APY doesn’t pay 5% per day – you get 1/365^{th} of 5% every day. Still, frequent compounding helps your money grow faster.
How to Calculate Compound Interest
There are several ways to calculate compound interest, giving you insight into how you can reach your goals, and helping you keep realistic expectations. Any time you run calculations, run a few “what-if” calculations using different numbers – see what would happen if you save a little more or earn interest for a few more years.
Online calculators are easiest, as they do the math for you and can easily create charts and year-by-year tables. But many people prefer to look at (and work with) the numbers more closely.
The formula for compound interest is:
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 due to rounding and the software you use for calculations). Of that amount, $1,000 is your initial deposit, and the remaining $1,114 is interest.
See a sample spreadsheet on Google Docs showing how it works, and download a copy to use 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 products offer this function – but you’ll need to adjust the numbers a bit.
Using the example above, let’s go through the calculation with Excel’s future value function:
=FV(rate,nper,pmt,pv,type)
It might be easiest to enter 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(rate,nper,pmt,pv,type)
- =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.
The Rule of 72 is another way to quickly make estimates about compound interest. 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. 72 divided by 5 is 14.4, so 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). 72 divided by 20 equals 3.6, so you’ll need to earn 3.6% APY to reach your goal.