# Quantitative - Simple and Compound Interest

## Simple and Compound Interest Description

1. Interest:- the money paid by the borrower to the lender.
There are two basis on which interest are calculated.

Simple Interest (S.I):- When interest is calculated on original principal at any length of time.

Compound Interest (C.I):- When at the end of the year or other fixed period the interest that has become due is not paid to the lender but is added to the sum lent, and the amount so obtained becomes the principal for next period.
The process is repeated until the amount for last period has been found.
The difference between original principal and amount is C.I.

2. Principal(P):- The money borrowed or lent out for a certain period is called the principal or the sum.

3. Rate(R):- Interest is usually calculated at the rate of so many rupees for every Rs.100 of the money lent for a year. This is called rate percent per annum.

4. Per Annum(p.a):- It means for a year.

5. Time(T):- Period at which amount to be returned.

6. Amount(A):- The sum of principal and interest.

Important Formulas
1. S.I = ${\frac{P\times R\times T}{100}}$

2. P = ${\frac{S.I\times 100}{R\times T}}$

3. R = ${\frac{S.I\times 100}{P\times T}}$

4. T = ${\frac{S.I\times 100}{P\times R}}$

5. When interest is compounded annually.
A = P${\left(\begin{array}{c}1+\frac{r}{100}\\ \end{array}\right)^{t}}$

6. When interest is compounded half yearly.
A = P${\left(\begin{array}{c}1+\frac{r}{200}\\ \end{array}\right)^{2t}}$

7. When interest is compounded quarterly.
A = P${\left(\begin{array}{c}1+\frac{r}{400}\\ \end{array}\right)^{4t}}$

8. When rate of interest is r1%, r2%, r3% for first, second, third year respectively.
A = P${\left(\begin{array}{c}1+\frac{r1}{100}\\ \end{array}\right)\left(\begin{array}{c}1+\frac{r2}{100}\\ \end{array}\right)\left(\begin{array}{c}1+\frac{r3}{100}\\ \end{array}\right)}$

9. C.I = A - P
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