Compound Interest

What Is Compound Interest?

Compound interest is interest earned on both the original amount of money, called the principal, and on the interest that has already been added to it. Because each round of interest is added to the balance, the next round is calculated on a larger amount. Growth therefore accelerates over time instead of staying the same amount each period.

Compound interest appears in savings accounts, certificate of deposit balances, and some bond reinvestment plans. It also works in reverse on debts such as credit card balances, where unpaid interest is added to what is owed.

How It Works

The standard formula for the future value of an investment with compound interest is:

A = P × (1 + r/n)^(nt)

Here, A is the amount after the period, P is the principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. All else being equal, the more often interest compounds, the faster the balance grows.

Compounding frequency varies. Interest may be compounded annually, quarterly, monthly, or daily. Annual percentage yield allows accounts that compound at different frequencies to be compared on an equal basis.

An Illustrative Example

Suppose $1,000 earns 5% interest compounded once a year. After the first year, it grows to $1,050. In the second year, interest is earned on $1,050 rather than $1,000, so the balance becomes $1,102.50. After ten years, with no additional deposits, the balance reaches about $1,628.89. With simple interest at the same rate, the balance would be $1,500 after ten years. The gap widens the longer money stays invested.

Why It Matters to Investors

Compound interest rewards time. Starting earlier and leaving earnings invested lets growth build on itself, which is why many investors study long-term investing as a concept. The same effect can work against borrowers, since interest on unpaid debt compounds too. Investors also consider inflation, because the real purchasing power of compounded returns depends on how prices change. Compound interest is a mathematical principle, not a guarantee of any particular return.