# Compound Interest  ## Compound Interest:

(1) Principal (P)- It is the money borrowed or lent out for a certain time.

(2) Interest (I)- It is the additional money that the lender receives from the borrower in consideration of the borrower using the money.

(3) Amount (A)- The sum of principal and interest is called amount.

(4) Rate of Interest (R)- Money paid per \$100 per year is called rate of interest.

(5) Time (T)- The period for which the money is borrowed or lent out is called time.

(6) Simple Interest (SI)- When the principal remains the same for the entire duration for which the money is lent (or borrowed) interest is calculated on the original principal for the given time and rate, this interest is known as simple interest. In other words, if the interest on a sum is calculated uniformly on the same sum, then it is called simple interest.

(7) Compound Interest (CI)- When the interest is earned over a fixed time (a year or any specified period such as six months, three months, etc.) is added to the principal for the next time period and this process is repeated for several time periods, the difference between the amount at the end of the last time period and the original principal is called the compound interest for the whole period.

The time period after which the interest is added to the original principal to form a new principal is called the conversion period. This period may be one year, six months, three months, or one month. Thus correspondingly, the interest is said to be compounded annually, semi-annually, quarterly, or monthly.

Note: In the case of simple interest, the principal remains the same for the whole duration whereas in the case of compound interest, the principal keeps changing periodically.

If the interest is payable yearly, then the compound interest for 1 year will be the same as the simple interest for 1 year.

The compound interest on a principal for two years is more than the simple interest on the same principal for two years.

Formulae for Compound Interest: