Compounding refers to the growth in the value of an investment where the return is being reinvested.
Compounding is the inverse operation to discounting.
Compound growth is exponential rather than linear. This means that the value of a compounded investment becomes disproportionally larger as time passes.
Suppose that an account earns 5% per year. We want to know how much $1,000 placed 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
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 the 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) sum one and the periodic interest rate, and (3) raise the result to the total number of compounding periods (years times the number of compounding intervals per year).
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