All Formula of simple and compound interest

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

(ii) Principal amount = (Simple interest ✕ 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


(i) When interest is payable annually, Then compound addition =



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

               ∴ Compound addition =



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

              ∴ Compound addition =


(iv) When time is a rational number, For example:- 




               ∴ Compound addition =

(v) When the first year of interest rate = R1 %, Second year = R2 %, third year = R3 %, then

                ∴ Compound addition =

2. Let any amount = x, payable after n years and interest rate = R % yearly, then

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