Interest: Simple & Compound

Interest or Simple Interest is the money/consideration paid by the borrower to the lender for the use of money lent for a specified period. The sum lent is called the Principal. Interest is calculated at a rate % for a certain period of time.
Simple interest : SI =
where SI is the Simple Interest, P the principal amount, T the time of year, R the rate %

The sum of the principal and the interest is called the Amount A = P + I

Important Points on Simple Interest
(1) Initial money that has been borrowed is called Principal or Sum.
(2) Interest is the reward for risk taking and is dividend on the Principal lent.
(3) When the interest is computed uniformly, it is called Simple Interest, or S.I.
(4) Amount = Principal + Interest. (5) Formulae:

Let Principal = P; Rate = R% and Time = T years. Then,
S.I. = ; P = ;
T = R =

Compound Interest: When the interest is earned on the already earned interest this is called a system of Compound Interest when interest is added to the sum lent, and the amount thus obtained becomes the principal for the next year or period. The system of adding interest to the principle thus calculated after addition of previous interest is repeated until the amount for the last period has been found. The difference between the final amount and the original principal is the Compound Interest (CI)
Formulae - Compound Interest:
Let, Principal = P, Time = n years & Rate = R % per annum. (1) When Interest is compounded Annually: Amount = P (2) When Interest is compounded Half-Yearly Rate will be halved and time (years) converted into half years. e.g. @8% for 1.5 years. It means now the rate will be 4% per half years for 3 half years. (3) When Interest is compounded Quarterly : Amount = P


These are paired quantities. One figure appearing anywhere will have an involvement of the remaining somewhere connected.
e.g. From the above table, 8000 given at 5% in 3 years will become 9261 or shall earn 1261 and so on.

Example: The simple interest on a sum of money is 1/9 of the principal, and the number of years is equal to the rate per cent per annum. Find the rate of per cent.

If the principal = P, Time = n years, Rate p.c. = n
then I = = ? n2 = ? = = 3 ?Rate p.c. is 3

Example: If Rs. 5600 amount to Rs. 6678 in 3 years, what will Rs. 9400 amount to in 5 years at the same rate per cent per annum, simple interest?
Solution
We first find the rate p.c.
Interest on Rs. 5600 = Rs. 6678 - Rs. 5600 = Rs. 1078
? rate % = = = × 5
Interest on Rs. 9400 = Rs. = Rs. 2714.25
? The required amount = Rs. 9400 + Rs. 2714.25 = Rs. 12114.25