# All Formula of simple and compound interest

## SIMPLE INTEREST

When a person borrows money from any bank, he has to pay extra money to use another's money, this extra money is called interest and the money borrowed is called

**principal money**.

The sum of the principal and interest is called the

**compound money**.

**Simple interest:-**The interest that is charged only on the principal at the same rate for a fixed period is called simple interest.

(i) Simple interest = (principal amount ✕ rate ✕ time)/100

**/**(rate ✕ time)

(iii) Rate = (Simple interest ✕ 100)

**/**(Principal amount ✕ time)

(iv) Time = (Simple interest ✕ 100)

**/**(Principal amount ✕ rate)

(v) Suppose any money is payable after T years and the rate of interest is R% per annum. Then

Instant money = (Owing money ✕ 100)

**/**100+( R ✕ T)

### COMPOUND INTEREST

Sometimes a fixed period is fixed for repaying the lending money. This period is usually

**yearly**or

**half-yearly**or

**quarterly**. After the end of this period, the compound formed after adding the interest to the principal becomes the principal for the next period.

This process is repeated for each period

The compound obtained at the end is called

**compound addition**.

**Compound interest = Compound addition - Principal amount**

__The formula for compound addition__

1. Considered principal = P, rate = R% , Annual and time = n years

(ii) When interest is payable half-yearly, Then rate = (R/2)% per half-yearly and time = (2n) half-yearly

(iii) When interest is payable quarterly, Then rate = (R/4)% per quarterly and time = (4n) quarterly

(v) When the first year of interest rate = R

_{1}%, Second year = R_{2}%, third year = R_{3}%, then
2. Let any amount = x, payable after n years and interest rate = R % yearly, then

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