Compound Interest


DEFINITION of 'Compound Interest'

Compound interest is 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.


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BREAKING DOWN '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.

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