## What is Compound Interest?

Compound interest refers to interest payments that are made on the sum of the original principal and the previously paid interest. An easier way to think of compound interest is that is it “interest on interest,” where the amount that the interest payment is based on changes in each period, rather than being fixed at the original principal amount.

Compound interest enables investors to earn potentially very high returns over a long time horizon and is essentially a risk-free way to generate gains. It is very different from equity investments, where capital gains are only realized if the security’s market value increases over time (i.e., buy low, sell high).

Compound interest isn’t entirely risk-free, as the interest payer can default or interest rates can change. However, the mechanism of compound interest is what makes it relatively riskless compared to other investments.

### Components of Compound Interest

The following are the four main components of compound interest:

#### 1. Principal

The principal is the amount that is originally deposited in a compounding environment (for example, a high-interest savings account at a bank). It is the starting amount upon which the first interest payment is calculated from.

#### 2. Interest rate

The interest rate refers to the rate that is paid on the account value. The interest payment will be equal to the interest rate times the account value (which is the sum of the original principal and any previously paid interest).

#### 3. Compounding Frequency

The compounding frequency determines how many times a year the interest is paid. It will influence the interest rate itself as high-frequency compounding will typically only be available with lower rates. Typically, compounding occurs on a monthly, quarterly, or annual basis.

#### 4. Time horizon

Time horizon refers to the amount of time over which the compound interest mechanism can operate. The longer the time horizon, the more interest payments that can be made to the original principal and the larger the ending account value will be.

Time horizon is the single most important component of compound interest, as it essentially dictates the future profitability of an investment. A compounding environment with low rates and low compounding frequency can still be attractive if the available time horizon is very long.

### Practical Example: Compound Interest

Sam wants to start saving and decides to deposit money into a high-interest savings account. He deposits an initial $20,000, which is to be compounded yearly at a rate of 3% per month. Sam is currently 20 years old and plans to retire at 60, which means that he can avail himself of a 40-year time horizon over which to accumulate interest.

Taking into account the given information, the table below calculates how much Sam’s account value would be at the end of his time horizon:

Here, we see that the account value at the end of the 40-year period is about $70,000. It shows the power of compound interest, as Sam was able to multiply his money seven-fold without actively managing the investment. We see how as interest accumulated on the principal, the interest payment in the succeeding period increased, thus fueling the cycle of compound interest.

The example above also assumes that Sam never deposited additional money into his savings account. Had Sam deposited an additional $20,000 early on in his time horizon, the final account value would have been dramatically higher.

### Related Readings

Thank you for reading CFI’s explanation of compound interest. CFI offers the Financial Modeling & Valuation Analyst (FMVA)™ certification program for those looking to take their careers to the next level. To keep learning and advancing your career, the following resources will be helpful: