DEFINITION
It is interest earned on the original principal plus interest accumulated.
Important Takeaways
Compound interest is interest paid on interest already earned.
Many banks compound interest daily, helping you grow your money more quickly.
Compound interest is simple to calculate using online calculators.
Save early to optimize your returns.
Compound Interest: Definition and Examples
It is interest earned on the original principal plus interest accumulated. You not only earn interest on your initial deposit, but you also make interest on the growth. It gets bigger at a faster rate as it increases.
What Is the Process of Compound Interest?
To grasp the notion of compound interest, first, learn the concept of simple interest: You make a deposit, and the bank pays you interest on that deposit.
For example, if you get 5% yearly interest, a $100 deposit will net you $5 after a year. What happens the next year? This is when compounding comes into play. You will earn interest on your initial deposit as well as interest on the growth you have already earned.
Because your account balance is now $105, rather than $100, the interest you earn the second year will be higher.
Note:
Even if you don’t make any more deposits, your earnings will grow faster with compound interest.
Year One: A $100 deposit generates 5% interest, or $5, raising your total balance to $105.
Year two: You earn 5% interest, or $5.25, on your $105 investment. Your account balance is $110.25.
Year three: Your $110.25 balance receives 5% interest, or $5.51. Your account balance rises to $115.76.
The above is an example of yearly compounded interest. Many institutions, especially online banks, compound interest daily and add it to your account monthly, making the process even faster.
Compounding, of course, works against you and in favor of your lender if you borrow money. You have to pay interest on the money you borrowed.
Compound Interest Calculator
There are various methods for calculating compound interest. Learning how to do it yourself can provide you with invaluable insight into how to meet your savings objectives while maintaining reasonable expectations. When performing computations, consider a few “what-if” scenarios with various numbers to see what would happen if you saved a little more or earned interest for a few years longer.
Note:
A compound interest calculator, such as ours, simplifies this computation by doing the math for you, allowing you to easily compare investment profits or borrowing expenses.
Some people choose to examine the figures in greater depth by completing their own calculations. You can use a financial calculator with formula storage functions or a normal calculator with an exponent key to calculate exponents.
To compute compound interest, use the following formula:
Compound Interest Calculator
To use this calculation, enter the following variables:
A: The whole amount you’ll receive.
P: The principle is your initial deposit.
r : The annual interest rate in decimal form.
n: the annual number of compounding periods (for example, monthly is 12, and weekly is 52).
t: the period of time (in years) it takes for your money to compound.
Performing the Math
You have $1,000 that is compounded monthly at 5%. How much money will you have in 15 years?
A = P (1 + [ r / n ]) ^ nt
A = 1000 (1 + [.05 / 12]) ^ (12 * 15)
A = 1000 (1.0041666…) ^ (180) (180)
A = 1000 (2.113703) (2.113703)
A = 2113.70
You’d have around $2,114 after 15 years. Because of rounding, your final figure may differ somewhat. The first $1,000 is your original deposit, and the remaining $1,114 is interest.
A Google Docs sample spreadsheet demonstrates how it works. There is also a downloaded version that you can use with your own numbers.
Making Use of Spreadsheets
Spreadsheets can perform all of the calculations for you. A future value calculation is typically used to compute your final balance after compounding. This function is available in Microsoft Excel, Google Sheets, and other software packages, however the numbers must be adjusted slightly.
Using the preceding example, you can perform the following calculation using Excel’s future value function:
The Future-Value Function in Excel
Fill in the blanks with each of your variables. Cell A1 may have “1000” to symbolize your original deposit, and Cell B1 could have “15” to signify 15 years.
The key to using a spreadsheet for compound interest is to think in terms of compounding periods rather than years. Because there are 12 months or “periods” in a year, the periodic interest rate for monthly compounding is just the annual rate divided by 12. Most firms utilize 360 or 365 for daily compounding.
=FV(rate,nper,pmt,pv,type)
=FV([.05/12],[15*12],1000,)
The pmt section, which would be a periodic contribution to the account, has been omitted in this example. This would be useful if you were adding money to the account on a monthly basis. In this scenario, type is also not used. If you wanted to conduct a calculation depending on when payments are due, you’d use this. 1
The 72-hour rule
Another method for calculating compound interest quickly is the Rule of 72. By looking at the interest rate and the length of time you’ll earn that rate, you may get a reasonable idea of how long it will take to double your money. Take the number of years and multiply it by the interest rate. If you get 72, you have a set of circumstances that will roughly treble your money. 2
Example 1: You have $1,000 in savings that earns 5% APY (annual percentage yield). How long will it take you to total $2,000 in your bank account?
Figure out how to get to 72 to find the answer. Because 72 divided by 5 equals 14.4, it will take approximately 14.4 years to quadruple your money.
Example 2: You currently have $1,000 and will require $2,000 in 20 years. What interest rate must you earn in order to double your money by then?
Again, given the information you have, calculate what it takes to get to 72, which is the number of years in this example. Because 72 divided by 20 = 3.6, you’ll need to earn 3.6% APY throughout that time period to reach your target.
What Does This Mean for Individual Investors and Savers?
There are ways for you, as an individual saver or investor, to ensure that compounding works in your benefit.
Save frequently and early.
Time is your friend when it comes to developing your money. Because compound interest multiplies money exponentially over time, the longer you can leave your money alone, the more it can grow.
If you deposit $100 each month for five years at 5% interest compounded monthly, you will have saved $6,000 in deposits and earned $800.61 in interest. Even if you never make another payment after that, your account would have earned an extra $7,573.87 in interest after 20 years – far more than your initial $6,000 in deposits, thanks to compounding.
Examine the APY
Examine the annual percentage yield while comparing bank products such as savings accounts and CDs. It accounts for compounding and delivers a true annual rate. Because the APY is higher than the interest rate, banks usually publicize it. You should aim to achieve good rates on your savings, but transferring banks for extra 0.10% is usually not worth it unless you have a very substantial account balance.
Pay off your debts early, and pay more when you can.
Paying the minimum on your credit cards will cost you a lot of money. You’ll barely make a dent in the interest payments, and your balance may even increase. Avoid capitalizing interest charges (adding unpaid interest charges to the debt total) if you have student loans, and at the very least pay the interest as it accrues to avoid a nasty surprise after graduation. Even if you are not forced to pay, you will benefit from lowering your lifetime interest costs.
Maintain Low Borrowing Rates
In addition to influencing your monthly payment, interest rates on your loans dictate how quickly your debt accumulates and how long it takes to pay it off. It’s challenging to deal with the double-digit interest rates that most credit cards have. Check to see whether it makes sense to consolidate debts and lower your interest rates while paying off debt; it could expedite the process and save you money.
What Makes Compound Interest So Effective?
When interest is paid repeatedly, it compounds. The first one or two cycles are not particularly striking, but the power of compound interest begins to emerge after interest is added repeatedly.
Frequency
The frequency of compounding is important. More frequent compounding periods, such as daily, have more dramatic outcomes. Look for daily compounding accounts when opening a savings account. Although you may only see interest payments transferred to your account on a monthly basis, calculations can still be performed on a daily basis. Some accounts only compute interest on a monthly or annual basis.
Over vast spans of time, time compounding becomes increasingly dramatic. When money is left alone to grow, you have a bigger number of calculations or “credits” to the account.
Rate of Interest
The interest rate also has a significant impact on your account balance over time. Higher rates suggest that an account will grow faster, but compound interest can compensate for a lower rate. An account compounding at a lesser rate can end up with a bigger balance than an account employing a simple formula, especially over long periods of time. Calculate the break-even threshold and the likelihood of that happening.
Withdrawals and deposits can both have an impact on your account balance. Allowing your money to grow or making frequent deposits to your account will work best. Withdrawing your earnings reduces the effect of compounding.
Amount to Begin With The amount of money you begin with has no bearing on compounding. Compounding works the same whether you start with $100 or $1 million. When you start with a high deposit, the results appear larger, but you are not punished for starting little or keeping accounts separate. When preparing for the future, it is best to concentrate on percentages and time: How much will you get paid and for how long? The money is simply a product of your rate and timeframe.