What Is Compound Interest?
Compound interest is interest earned on interest. It occurs when interest is reinvested and allowed to accumulate and grow on itself. It is interest earned on the initial principal invested plus interest earned on interest that is reinvested at the end of each period.
Why Is Compound Interest Important?
When interest is compounded, it means investments grow at a greater rate than if interest were just paid on the principal amount alone. It allows an investment to build on itself and increasingly grow its earnings over time. This means compound interest yields a greater return than simple interest.
Compound Interest Vs. Simple Interest
Simple interest is paid on the principal amount only. It is not paid on the interest earned. Since interest earned is not reinvested, there is not the advantage of allowing interest to earn interest on itself.
To illustrate, if $100,000 were invested for a year at 10% interest, then the investment would yield $10,000. In simple interest, it works as if the interest is withdrawn each time interest is paid.
Compound interest builds upon itself over multiple periods. Simple interest is earned for each period, but you do not reinvest any interest earned. Any subsequent period earns interest only on the principal invested.
Compounding Periods
Compounding Periods are the interval at which interest is paid. Compounding periods are often monthly, quarterly, or annually, but can be for any interval. At the end (or sometimes beginning) of each period, interest is paid and added to the principal investment. In the next period, interest is paid on the principal plus the accumulated interest earned in the previous period.
The result is interest is paid and the growth of the investment increases at an increasing rate over time. This is in contrast to simple interest which on a graph appears as a straight line. The rate of growth in simple interest does not increase. The more compounding periods in an investment, the greater the rate of growth over time.
Interest Rates And Compound Interest
There is a bit of complexity in understanding interest rates as they apply to compound interest. For example, the stated interest rate is not necessarily the interest rate earned. In this case, if the annual interest is stated at 12%, but interest is compounded monthly, the interest earned will be greater than 12% at the end of the year.
The other key issue to understand is the stated interest rate is not necessarily the interest rate paid each period. In the example above, if the annual interest rate is 12% compounded monthly. The monthly periodic rate is 1%. The means every month, the investment will earn 1% on top of the principal and accumulated interest earned the month before.
Nominal Annual Interest, Periodic Interest, and Effective Interest Rates
To clarify the issues of compounding regarding the interest rate, it is worthwhile to review a few vocabulary terms. The nominal interest rate is the stated interest rate for a period of time. If the nominal rate is for a year, it is termed the nominal annual rate. It is the interest rate "in name only."
The periodic interest rate is the interest rate applied to each compounding period. To illustrate, if the nominal annual rate is 12% and the interest is compounded monthly, the periodic interest rate is 1%.
The periodic interest rate in the example is calculated by dividing the nominal annual rate by the number of compounding periods per year. There are 12 months per year and the nominal annual rate is 12%. The periodic rate = 12% / 12 months = 1% per month.
The effective annual rate is the total interest actually earned expressed as a percentage rate of the principal invested. In our example, if we invested $100 at 12% for a year compounded monthly, we'd have $112.68 at the end of the year. The total amount of interest earned is $12.68. This is more than the nominal annual rate of 12% implies. Since we actually earned $12.68 on our investment of $100 thanks to our compounded interest, our effective annual rate is 12.68%.