What Is Compounding?
Compounding refers to the growth in the value of an investment when the return is being reinvested.
Compound growth is exponential rather than linear. This means that the value of a compounded investment becomes disproportionally larger as time passes.
This concept is a core part of fundamental investing.
Example of Compounding
Suppose that an account earns 5% per year. We want to know how much $1,000 put into this account will be at the end of five years. We can calculate the growth of the account by multiplying the initial investment by a compounding factor. To compute the compounding factor, we raise the sum of one and the interest rate to a power equal to the number of years. The compounding factor for the above example is 1.27628 (1.05 raised to the 5th power). We then multiply the starting investment by the compounding factor:
$1,000 x 1.27628 = $1,276.28
Compounding with Multiple Periods
In the above example, the account is compounded once per year. However, some investments may compound more frequently, such as quarterly or monthly. When there is more than a single compounding period in a year, we calculate the compounding factor with the following steps: (1) calculate the periodic rate by dividing the annual interest rate by the number of compounding periods in the year, (2) add one and the periodic interest rate, and (3) raise the result to the total number of compounding periods (number of years times the number of compounding periods in a year).
Example of Quarterly Compounding
Suppose that in the above example, the account compounds quarterly instead of yearly. The periodic rate is 0.0125 (.05 divided by 4) and the total number of compounding periods is 20 (four compounding periods times five years), so the compounding factor is 1.0125 raised to the 20th power, or 1.28204. The value of the account at the end of year five is $1,000 x 1.28204 = $1,282.04
Key Takeaways
- Compounding refers to investment growth where returns are reinvested.
- Compounded growth increases exponentially over time.
- The compounding factor is calculated by raising one plus the interest rate to the number of periods.
- Investments that compound more frequently grow faster than those compounded less frequently.
- Compounding is a key concept in finance and investment analysis.