Compound Interest

AAA

DEFINITION of 'Compound Interest'

Interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Compound interest can be thought of as “interest on interest,” and will make a deposit or loan grow at a faster rate than simple interest, which is interest calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period. Compound interest is also known as compounding.

INVESTOPEDIA EXPLAINS 'Compound Interest'

The formula for calculating compound interest is:

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)

                                = [P (1 + i)n] – P

                                = P [(1 + i)n – 1]

(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.)

If the number of compounding periods is more than once a year, "i" and "n" must be adjusted accordingly. The "i" must be divided by the number of compounding periods per year, and "n" is the number of compounding periods per year times the loan or deposit’s maturity period in years.

For example:

  • The compound interest on $10,000 compounded annually at 10% (i = 10%) for 10 years (n = 10) would be = $25,937.42 - $10,000 = $15,937.42
  • The amount of compound interest on $10,000 compounded semi-annually at 5% (i = 5%) for 10 years (n = 20) would be = $26,532.98 - $10,000 = $16,532.98
  • The amount of compound interest on $10,000 compounded monthly at 10% (i = 0.833%) for 10 years (n = 120) would be = $27,070.41 - $10,000 = $17,070.41

Compound interest can significantly boost investment returns over the long term. While a $100,000 deposit that receives 5% simple interest would earn $50,000 in interest over 10 years, compound interest of 5% on $10,000 would amount to $62,889.46 over the same period.

While the magic of compounding has led to the apocryphal story of Albert Einstein supposedly calling it the eighth wonder of the world and/or man’s greatest invention, compounding can also work against consumers who have loans that carry very high interest rates, such as credit-card debt. A credit-card balance of $20,000 carried at an interest rate of 20% (compounded monthly) would result in total compound interest of $4,388 over one year or about $365 per month.

VIDEO

RELATED TERMS
  1. Compound Annual Growth Rate - CAGR

    The year-over-year growth rate of an investment over a specified ...
  2. Interest Expense

    The cost incurred by an entity for borrowed funds. Interest expense ...
  3. Anticipated Interest

    The amount of interest that a savings vehicle will accrue by ...
  4. Compound

    The ability of an asset to generate earnings, which are then ...
  5. Interest

    1. The charge for the privilege of borrowing money, typically ...
  6. Interest Rate

    The amount charged, expressed as a percentage of principal, by ...
Related Articles
  1. What are the tax implications of a life ...
    Insurance

    What are the tax implications of a life ...

  2. Will debt consolidation stop debt collectors ...
    Credit & Loans

    Will debt consolidation stop debt collectors ...

  3. Is it easier to save for retirement ...
    Retirement

    Is it easier to save for retirement ...

  4. It's Never Too Early To Start Saving
    Savings

    It's Never Too Early To Start Saving

Hot Definitions
  1. Debit Spread

    Two options with different market prices that an investor trades on the same underlying security. The higher priced option ...
  2. Leading Indicator

    A measurable economic factor that changes before the economy starts to follow a particular pattern or trend. Leading indicators ...
  3. Wage-Price Spiral

    A macroeconomic theory to explain the cause-and-effect relationship between rising wages and rising prices, or inflation. ...
  4. Accelerated Depreciation

    Any method of depreciation used for accounting or income tax purposes that allows greater deductions in the earlier years ...
  5. Call Risk

    The risk, faced by a holder of a callable bond, that a bond issuer will take advantage of the callable bond feature and redeem ...
  6. Parity Price

    When the price of an asset is directly linked to another price. Examples of parity price are: 1. Convertibles - the price ...
Trading Center