• Compounding is the process whereby interest is credited to an existing principal amount as well as to interest already paid.
• Compounding thus can be construed as interest on interest—the effect of which is to magnify returns to interest over time, the so-called “miracle of compounding.”
• When banks or financial institutions credit compound interest, they will use a compounding period such as annual, monthly, or daily.
• Compounding may occur on investment in which savings grow more quickly or on debt where the amount owed may grow even if payments are being made.
• Compounding naturally occurs in savings accounts; some investments that yield dividends may also benefit from compounding.

Compounding typically refers to the increasing value of an asset due to the interest earned on both a principal and accumulated interest. This phenomenon, which is a direct realization of the time value of money (TMV) concept, is also known as compound interest.

Compounding is crucial in finance, and the gains attributable to its effects are the motivation behind many investing strategies. For example, many corporations offer dividend reinvestment plans (DRIPs) that allow investors to reinvest their cash dividends to purchase additional shares of stock. Reinvesting in more of these dividend-paying shares compounds investor returns because the increased number of shares will consistently increase future income from dividend payouts, assuming steady dividends.

Investing in dividend growth stocks on top of reinvesting dividends adds another layer of compounding to this strategy that some investors refer to as double compounding. In this case, not only are dividends being reinvested to buy more shares, but these dividend growth stocks are also increasing their per-share payouts.

The formula for the future value (FV) of a current asset relies on the concept of compound interest. It takes into account the present value of an asset, the annual interest rate, the frequency of compounding (or the number of compounding periods) per year, and the total number of years. The generalized formula for compound interest is:

This formula assumes that no additional changes outside of interest are made to the original principal balance.

The effects of compounding strengthen as the frequency of compounding increases. Assume a one-year time period. The more compounding periods throughout this one year, the higher the future value of the investment, so naturally, two compounding periods per year are better than one, and four compounding periods per year are better than two.

To illustrate this effect, consider the following example given the above formula. Assume that an investment of $1 million earns 20% per year. The resulting future value, based on a varying number of compounding periods, is:

• Annual compounding (n = 1): FV = $1,000,000 × [1 + (20%/1)] ^{(1 x 1)} = $1,200,000
• Semi-annual compounding (n = 2): FV = $1,000,000 × [1 + (20%/2)] ^{(2 x 1)} = $1,210,000
• Quarterly compounding (n = 4): FV = $1,000,000 × [1 + (20%/4)] ^{(4 x 1)} = $1,215,506
• Monthly compounding (n = 12): FV = $1,000,000 × [1 + (20%/12)] ^{(12 x 1)} = $1,219,391
• Weekly compounding (n = 52): FV = $1,000,000 × [1 + (20%/52)] ^{(52 x 1)} = $1,220,934
• Daily compounding (n = 365): FV = $1,000,000 × [1 + (20%/365)] ^{(365 x 1)} = $1,221,336

As evident, the future value increases by a smaller margin even as the number of compounding periods per year increases significantly. The frequency of compounding over a set length of time has a limited effect on an investment’s growth. This limit, based on calculus, is known as continuous compounding and can be calculated using the formula:

In the above example, the future value with continuous compounding equals: FV = $1,000,000 × 2.7183 ^{(0.2 x 1)} = $1,221,403.

Compounding is an example of "the snowball effect" where a situation of small significance builds upon itself into a larger, more serious state.

Compound interest works on both assets and liabilities. While compounding boosts the value of an asset more rapidly, it can also increase the amount of money owed on a loan, as interest accumulates on the unpaid principal and previous interest charges. Even if you make loan payments, compounding interest may result in the amount of money you owe being greater in future periods.

The concept of compounding is especially problematic for credit card balances. Not only is the interest rate on credit card debt high, the interest charges may be added to the principal balance and incur interest assessments on itself in the future. For this reason, the concept of compounding is not necessarily "good" or "bad". The effects of compounding may work in favor of or against an investor depending on their specific financial situation.

The Rule of 72 is a heuristic used to estimate how long an investment or savings will double in value if there is compound interest (or compounding returns). The rule states that the number of years it will take to double is 72 divided by the interest rate. If the interest rate is 5% with compounding, it would take around 14 years and five months to double.

Simple interest pays interest only on the amount of principal invested or deposited. For instance, if $1,000 is deposited with 5% simple interest, it would earn $50 each year. Compound interest, however, pays “interest on interest,” so in the first year, you would receive $50, but in the second year, you would receive $52.5 ($1,050 × 0.05), and so on.