# CLASS-9COMPOUND INTEREST

COMPOUND INTEREST

We know that, in post offices, banks, Insurance, non-banking & small finance corporations, and all those companies which lend money and accept deposits, the method of calculating interest is absolutely different from each other. Under this method, the borrower and the lender agree to fix a certain unit of time, it may be one year or a half year or one quarter of any of the year (3 months), to settle the previous account. In such cases, the interest accrued during the first unit of time is not given to the moneylender, but it is added to the original principal, and the obtained amount is to be considered or would be taken as the principal for the second unit of time. The amount of this principal at the end of the second unit of time becomes or will be considered as the principal for the third unit of time, and so on. After a certain specified period, the difference between the amount and the money borrowed will be considered or called the compound interest (abbreviated as C.I) for that period. This fixed unit of time is known or will be considered as the conversion period. For our better understanding, we can furnish some examples-

There are some rules, such as –

a) If the interest is compounded annually, then the conversion period is 1 year. The amount after 1 year becomes the principal for the second year. The amount after 2 years becomes the principal for the third year and so on.

b) If the interest is compounded half-yearly, then the conversion period is half-year. The amount after the first half-year becomes the principal for the second half-year. The amount after one year becomes the principal for the third half year and so on.

Compound Interest

1) Compound interest is a repeated simple interest computation with a growing principal. Use of this in computing amount over a period of 2 or 3 years.

2) Compound interest as a repeated simple interest computation with a growing principal. Use of this in computing amount over a period of 2 or 3 years.

Use of formula, A = P ( 1 + r/100 )ⁿ, Compound Interest (C.I) = A – P

Interest compound half-yearly included using the formula to find one quantity given different combinations of A, P, r, n, C.I, and S.I. difference between C.I and S.I type included.

Example.1)  Find the amount and the compound interest on \$ 1200 for 3 years at 10% per annum, compound annually.

Ans.)   Principal for the 1st year = \$ 12000

10

Interest for the 1st year = \$ ( 12000 X ------- X 1 ) = \$ 1200

100

Amount at the end of 1st year = \$ ( 12000 + 1200 ) = \$ 13200

So, principal for the 2nd year = \$ 13200

10

Interest for the 2nd year = \$ ( 13200 X ------- X 1 ) = \$ 1320

100

Amount at the end of 2nd year = \$ ( 13200 + 1320 ) = \$ 14520

So, principal for the 3rd year = \$ 14520

10

Interest for the 3rd year = \$ ( 14520 X ------- X 1 ) = \$ 1452

100

Amount at the end of 3rd year = \$ ( 14520 + 1452 ) = \$ 15972

Cumulative Interest (C.I) after 3rd year =

=> Amount (A) – Original Principal (P)

=>  \$ (15972 – 12000) = \$ 3972

So, the required amount (A) after 3rd year is = \$ 15972, and the compound interest (C.I) = \$ 3972     (Ans.)