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# What is compound interest?

### Interest

Interest plays a very important part in investments. Money is being lent or borrowed by individuals, banks or other financial institutions for a consideration known as interest. Where, P= amount give to borrower, also called principal amount.
R=Interest earned on amount P and also known as charges.
The rate of interest is also decided between them. Interest is charged because of the time value of money.

### Term to remember

• Principal (P): The amount of money that is originally invested or loaned (lent or borrowed) is called the principal (or the present value of the money).
• Interest (I): Interest is consideration (or fee) for the use of invested or loaned (capital or principal).
• Time (T): The time is the number of years or fraction of a year for which the principal is borrowed or loaned.
• Amount (A): The amount is the sum of the principal and the interest earned in the specified time and also known as accrued amount (or the future value).

### Rate of Interest

It is the money payable for the use of unit principal for unit interval of time (unit interval of time : years, six months, three months or a month). Correspondingly rate of interest is payable annually (per annum or p.a.), half-yearly (or semi-annually), quarterly or monthly.

### Rate of Interest

There are two important kinds of interest such as;

• Simple Interest
• Compound Interest

Simple Interest In simple interest the principal remains the same throughout the term of the loan. For example simple interest on Rs.100 at 6% per annum will be Rs.6 each year, i.e., at the end of the first year, the total amount will be Rs.106 and at the end of the second year it will be Rs.112 and so on. If Rs. P be the given principal loaned at the rate R% per annum for a period of T years. Then simple interest, I =PRT (I is multiplication of P x R x T)

Compound Interest Compounding interest is the second method for borrowing or lending money on interest. In this case principal keeps on changing at the end of each period of time. Concept of compounding interest is very important not only for those who are planning a career in financial institutions but even for ordinary investors who wish that their savings keep on growing steadily and he same become a source of income for them.

Compounded annually Compounded half yearly Compounded quarterly
N=1year; I=10% N=1year; I=10% N=1year; I=10%
N=1 ,I=10% N=1 x 2= 2 ,I= 10% x 1/2 N=1 x 4=4, I=10% x 1/4

In compound interest, unpaid interest over any unit of time, also earns interest over the subsequent units of time.

### Interest compounding continuously

When ‘N’ becomes larger and larger and we compute the interest, the more will be the compounding amount. In compound interest the principal doesn’t remains the same throughout the term of the loan. For example compound interest on Rs.100 at 10% per annum will be Rs.10 for first year, i.e., at the end of the first year, the total amount will be Rs.110 and at the end of the second year it will be the total amount at the beginning of the second year plus the rate of interest, i.e., Rs.110/- + 10% on Rs.110 which is equal to Rs.121/-p and so on. If Rs. P be the given principal loaned at the rate R% per annum for a period of T years.
Then simple interest, I =PRT (I is multiplication of P x R x T)CI = P (1+R) N
Where; CI=Compound Interest P = Principal R = Rate of Return N = Number of Years.

Example
Below given example will help you to understand the difference in growth of Rs. 100000 in simple interest and compound interest during a period of 10 years. The interest rate is assumed as 10% per annum.

Year Simple interest (10%) Compound Interest (10%)
1 110000 110000
2 120000 121000
3 130000 133100
4 140000 146410
5 150000 161051
6 160000 177156
7 170000 194871
8 180000 214358
9 190000 235794
10 200000 259374

In simple interest rate your Rs. 100000 has grown to Rs.200000 over a period of 10 years. But the same amount has grown to Rs. 259374 with a compound interest rate.