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Compound interest (and its sister compound growth) is an important concept associated with accumulating wealth. As a saver and investor, I've experienced the power of compounding. My savings started small. But over time, it has grown exponentially.
But how does compound interest work?
I'll explain and give examples to illustrate how compounding works, both for a single deposit in a savings account with a hypothetical interest rate and a stream of contributions to an investment account with a hypothetical growth rate. In addition, I'll provide a compound interest formula for both scenarios.
Compound Interest Explained
Compound interest is interest earned on savings and interest earned on interest. Generally, I think of interest as earnings on money held in a savings account.
Compound growth follows the same logic as compound interest. Compound growth represents earnings associated with dividends and capital gains on investments and earnings on dividends and capital gains.
A key difference is that investment growth rates are unpredictable whereas interest rates tend to be fixed, at least for certain periods of time. For my illustrations, I'm going to assume steady rates of interest and growth simply for the purpose of showing how compound interest works.
Compound Interest on a Single Deposit
Let's see how interest is compounded when you make a single deposit and earn 1% interest over 30 years.
First consider the interest as it compounds year after year using a spreadsheet:
In this illustration, you receive $50 interest in the first year ($5,000 x 1% = $50). In subsequent years, interest received grows as your account balance grows. By year 30, you'll receive $66.73 interest and your $5,000 has grown to $6,739.24.
I love spreadsheets as they allow me to model complex ideas (like compound interest) in an easy to understand way.
But I also like shortcuts, such as the Future Value (FV) function in spreadsheets offered by Microsoft Excel and Google Sheets. Here's how you can use this function to project the compounded value of an initial deposit over a number of years at a specified interest rate:
- =FV(Interest_Rate, Number_of_Years, Annual_Deposit, -Present_Value)
The interest rate in this FV formula is 1%; the number of years, 30; the regular payment amount, $0, because you won't make annual contributions; and present value of the initial deposit, -$5000. (You have the option of specifying “0” or “1” for “type” to indicate whether a payment is made at the end or beginning of the time period; in this example, the type doesn't influence the result.) The future value is $6,739.24 using this formula.
You might also want to use a more traditional compound interest formula that doesn't use financial functions. Here's a formula for compound interest on a single opening deposit:
- Future Value = Initial_Deposit x [(1 + Interest_Rate) to the Power of the Number_of_Years]
- Future Value = $5,000 x [(1+.01) to the Power of 30]
- Future Value = $5,000 x [1.01 to the Power of 30]
- Future Value = $5,000 x Power(1.01,30)
- Future Value = $5,000 x 1.347848915
- Future Value = $6,739.24
Again, the initial deposit is equal to $5,000; interest rate, 1%; and the number of years, 30. The formula enables you to determine the exponential growth of the interest (that is, the value of 1% compounded over 30 years) and apply that number to determining the future value of your deposit.
In these examples, I've compounded interest on a yearly basis. You can make these scenarios more complex, compounding interest monthly rather than annually for example.
Compound Growth for Annual Deposits
Let's study how compounding works when you make an annual deposit for many years and experience consistent growth over a long period of time.
For example, let's say you invested $5,000 every year at the end of each year for 30 years and earned 10% every year. The compound growth would look like this:
The calculation using the Future Value (FV) function looks like this:
- =FV(Interest_Rate, Number_of_Years, -Annual_Deposit, Present_Value, 0_if_Interest_Paid_at_End_of_Year)
In this scenario, the interest rate is 10%; number of years, 30; annual deposit, $5,000; present value, $0; and the payment or annual deposit is timed at the end of the year (and doesn't draw interest or growth until the following year).
A more traditional compound interest formula is:
- Future Value = Annual_Deposit x ((Power(1+Interest_Rate, Number_of_Years)-(1))/Interest_Rate)
- Future Value = 5000 x ((POWER(1+10%,30)-(1))/10%)
- Future Value = 5000 x ((17.44940227)-(1))/10%)
- Future Value = 5000 x ((16.44940227)/10%)
- Future Value = 5000 x 164.4940227
- Future Value = $822,470.11
Again, the annual contribution is $5,000; interest rate, 10%; and number of years, 30.
The best description of this formula that I could find comes from MoneyChimp.com at a page dedicated to Basic Investment formulas for growth and contributions.
There, you can also find explanations and formulas that apply when contributions are made at the start of each year. For example, the future value of contributions with interest applied at the beginning of the year (that is, =FV(10%,30,-5000,0,1) equals $904,717.12. A more traditional compound interest formula is Annual_Deposit x ((Power(1+Interest_Rate,Number_of_Years+1)-(1+Interest_Rate))/Interest_Rate) or =5000 x ((Power(1+10%,30+1)-(1+10%))/10%), which also equals $904,717.12.
Finally, if you'd like to see the spreadsheet showing the progression to this number, here it is:
As I mentioned earlier, a steady growth rate of 10% annually over 30 years is not a representation of real-world probability but an illustration of the power of compound growth.
As a business-finance major, I like to design spreadsheets occasionally to model how compounding works. But, generally, the easiest way for me to project the value of a stream of payments is to use the Future Value function. After you see the numbers in action, you may be able to better understand and use compounding interest to your advantage, possibly by investing as soon as possible to gain from growth over time.