Compound Interest

Compound interest is a type of interest where in the interest added to the principal amount also earns interest starting from the time when it is added to the principal amount.Payments or investments using compound interest are done in a periodical manner. The interest earned in the period will be added to the principal amount and both will earn interest in the next period. This manner is called compounding wherein accumulated interest from previous periods will also earn interest as it goes along the succeeding payments.

For example: if the initial principal amount is $1000 and some financial institution is paying 10% interest per year, then at the end of first year the interest earned will be $1000 * 10/100 = $100. Hence the total principal amount at the end of the year will be $1000 +$100 = $1100.

When dealing with Compound Interest, next year the interest amount will be calculated using $110 as initial principal amount. Hence the interest earned at the second year will be $1100 * 10/100 = $110 So, principal amount at the end of second year will be $1210.

The increase of the amount is not constant since the interests paid also earn interest. Most of the times, banks and loaning agencies apply this type of interest especially for long term transactions.

Terms to remember

Compound - to put or add together
Loan - the exponent required to raise the base in order to produce a given number.
Logarithm a whole number and a proper fraction. Ex. 1 2/3
Nominal - named or bearing the name of a specific person or thing.
Period - amount of time
Quarter - one-fourth of a year which is 3 months
Ratio relationship between two numbers. Ex. 1:2

Distinguishing Compound Interest from Simple Interest

Simple interest and compound interest differs in many aspects. Here are some of their differences:

  • Compound interest is earned periodically. Simple interest is earned only once within the agreed period of payment.
  • Compound interest increases exponentially period after period. Simple interest grows in a consistent manner.
  • Rateof simple interest isannual. Compound interest rates can be yearly, monthly, quarterly, weekly etc.
  • Total amount earned or paid using simple interest is less as compared to the total amount earned or paid using compound interest.
  • Simple interest is usually used for short term transactions since it earns less. Compound interest is preferable for long term transactions to increase wealth.
  • Calculation for future amount in compound interest is complex than with simple interest since it involves division and exponents.

Terms related with Compound Interest

Similar to simple interest, the same common factors affect compound interest but there are some additional things that should be taken into account.

  • Principal : This is the amount which is being invested or borrowed. This amount increases periodically as interest accumulated in each period is added to the principal as the new principal amount.
  • Compounding : Unlike simple interest, the rate of interest (nominal) should be divided by the number of periods that the interest would be compounded in a year.
    For example:
  • Rate of Interest : This is the percent rate to be used to calculate the additional amount to be earned or paid for using the money. The rate of interest to be used for each period depends on the manner that the interest is being compounded. The formula for calculating the rate of compound interest is:
  • Rate per Period ` = text(Nominal Rate)/text(Periods per Year)`

    Note: The nominal rate of interestis the annual interest rate.

  • Number of Periods The period in compound interest is not the entire duration of the transaction but it is the time interval in which the compound interest will be applied. The formula for getting the number of periods is:
Number of Periods = Periods per Year x Number of Years

For example:
10% compounded monthly for 2 years Compound interest is applied every month. Therefore, the number of periods would be 12 months/year x 2 years = 24.

Example 1:

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