# SIMPLE INTEREST & COMPOUND INTEREST

## SIMPLE INTEREST

The Initial money borrowed or lent out for a certain period is called the Principal (P).

The extra money paid for using others money is called Interest.

The total money paid back to the lender at the end of the time period(T) for which the principal is borrowed is called an amount (A).

The rate at which the interest has to be paid per annum is called rate of interest (R).

Simple Interest :- If the interest is calculated every year on the initial money borrowed, then it is called Simple Interest (S.I.)

Here the interest remains the same for every year as it is calculated on the original money borrowed.

Amount = Principal + Simple Interest

Simple Interest can be calculated by the following formula:

SI = P * R * T /100

P = 100 * SI / R * T

R = 100 * SI / P * T

T = 100 * SI / R * P

here time period (T)  in years

A = P + SI

= P + {P*R*T/100} = P[1 + (RT/100)] = P[(100+RT)/100]

P = [(100*A)/(100+RT)]

NOTE: While calculating the time period between two given dates, the day on which money is deposited is not reckoned while the day on which money is withdrawn, is counted.

## COMPOUND INTEREST

The phrase ‘Time is Money ‘ is apt for the calculation of compound interest. The interest accured is added to the principal at the end of the first year, this amount becomes principal for second year and so on. The final interest thus calculated is called the compound interest. In other words, the difference between final amount and original principal is called compound Interest (CI).

• In case of simple interest, the principal remains uniform whereas in case of compound interest, the principal changes.
• In case of compound interest, the interest becomes part of the investment, so that interest is earned on the interest itself.
• The interest is said to be compounded annually if the principal changes every year.
• Then the amount = P[1+(R/100)]n  where P is principal in Rs., time is n years and rate R % p.a.
• The interest is said to be compounded half yearly or semi annually, if the principal changes every six months  then the amount  = P{1+[(R/2)/100]}n  where P is principal in Rs., time is n years and rate R % p.a.
• The interest is said to be compounded quarterly , if the principal changes every six months  then the amount  = P{1+[(R/4)/100]}n  where P is principal in Rs., time is n years and rate R % p.a.
• When Rate of Interest is R1%, R2%, and R3% for first year , second year and third year respectively , then amount = P[1+R1(/100)][1+R2(/100)][1+R3(/100)]
• When the value of particular item depreciates every term at fixed rate, then the amount = P[1-(R/100)]n. In this case, the principal goes on reducing every term by a fixed rate.
• The difference between the Simple Interest and Compound Interest for 2 term is given by D = P(R/100)2, Where, D is the difference,  P is Principal and R is the rate of interest.