Loading the player...

What is 'Compounding'

Compounding is the process in which an asset's earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods. Compounding, therefore, differs from linear growth, where only the principal earns interest each period.

BREAKING DOWN '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. 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.

To illustrate how compounding works, suppose $10,000 is held in an account that pays 5% interest annually. After the first year, or compounding period, the total in the account has risen to $10,500, a simple reflection of $500 in interest being added to the $10,000 principal. In year two, the account realizes 5% growth on both the original principal and the $500 of first-year interest, resulting in a second-year gain of $525 and a balance of $11,025. After 10 years, assuming no withdrawals and a steady 5% interest rate, the account would grow to $16,288.95.

Compounding as the Basis of Future Value

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, and the frequency of compounding (or number of compounding periods) per year and the total number of years. The generalized formula for compound interest is:

FV = PV x [1 + (i / n)] (n x t), where:

  • FV = future value
  • PV = present value
  • i = the annual interest rate
  • n = the number of compounding periods per year
  • t = the number of years

Example of Increased Compounding Periods

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

FV = PV x e (i x t), where e = the irrational number 2.7183.

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

Example of Compounding for Investing Strategy

Compounding is crucial to finance, and the gains attributable to its effects are the motivation behind many investing strategies. For example, many corporations offer dividend reinvestment plans 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.

RELATED TERMS
  1. Compound

    Compound is the ability of an asset to generate earnings, which ...
  2. Effective Annual Interest Rate

    The effective annual interest rate is an investment's annual ...
  3. Time Value of Money - TVM

    The time value of money is the idea that money presently available ...
  4. Biotech Compound

    A biotech compound is a chemical identified by scientists as ...
  5. Automatic Reinvestment Plan

    An automatic reinvestment plan is a mutual fund plan that automatically ...
  6. Future Value - FV

    Future value (FV) is the value of a current asset at a date to ...
Related Articles
  1. Investing

    Overcoming Compounding's Dark Side

    Understanding how money is made and lost over time can help you improve your returns.
  2. Personal Finance

    How Interest Rates Work on Savings Accounts

    Here's what you need to know to grow your rainy-day fund so you needn't fear a little downturn.
  3. Managing Wealth

    APR and APY: Why Your Bank Hopes You Can't Tell the Difference

    Do you know the difference between Annual Percentage Rate and Annual Percentage Yield? Check out how they can affect your own account balance.
  4. Investing

    4 Ways Simple Interest Is Used In Real Life

    Simple interest works in your favor when you're a borrower, but against you when you're an investor.
  5. Retirement

    Compounding Is Important in the Later Years Too

    The power of compounding is even greater in the later years of saving for retirement.
  6. Investing

    Let the Power of Compounding Increase Your Investments

    The power of compounding can exponentially increase the value of your investments over time.
  7. Investing

    How to Make the Time Value of Money Work for You

    How to make the time value of money and power of compounding work for you. Here's a hint: Start saving now.
  8. Investing

    Investing $100 a Month in Stocks for 20 Years

    Learn how a monthly investment of just $100 can help build a future nest egg using properly diversified stocks or stock mutual funds.
RELATED FAQS
  1. How do I use the rule of 72 to calculate continuous compounding?

    The rule of 72 is a mathematical shortcut used to predict when a population, investment or other category will double in ... Read Answer >>
  2. How do I calculate compound interest using Excel?

    Learn how to calculate compound interest using three different techniques in Microsoft Excel. Read Answer >>
  3. Compound interest versus simple interest

    Simple interest is only based on the principal amount of a loan, while compound interest is based on the principal amount ... Read Answer >>
  4. Stated Annual Return vs Effective Annual Return

    The difference between these two measures is the effective annual return accounts for intra-year compounding, and the stated ... Read Answer >>
Trading Center