##
**Simple
Interest**

**Interest**is the additional sum of money to be paid for the use of money from a bank or money lender for certain period of time. Similarly, if we keep money in a bank or lend to someone else, we will be paid interest.

**Interest**is calculated on the basis of the initial sum of money, period of time and the rate of interest. When the interest calculated for certain sum of money is same for every year, it is called

**simple interest**.

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**Simple
Interest Formula**

Simple interest is given by the formula,

where, I ---------------> Simple Interest

P ---------------> Principal
(initial sum of money)

T ---------------> Time (in year)

R ---------------> Rate of
interest (in % per year)

A ---------------> Amount (sum of
principal and interest)

Some other formula,

**A = P + I**,

**I = A – P**,

**P = A – I**

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*Workout
Examples*

*Workout Examples*

*Example 1: Find the simple interest of Rs. 7500 for 5 years at the rate of 4% per annum. Also find the amount.*

*Solution:*

*Here,*

*P = Rs. 7500*

*T = 5 years*

*R = 4%*

*I = ? A = ?*

*We know,*

*A = P + I*

*= Rs. 7500 + 1500*

*= Rs. 9000*

*∴*

*Simple interest is Rs. 1500 and amount is Rs. 9000.*

*Example 2: Find the rate of interest per annum of Rs. 32500 amounts of Rs. 40625 in 5 years.*

*Solution:*

*Here,*

*P = Rs. 32500*

*A = Rs. 40625*

*T = 5 years*

*R = ?*

*We have,*

*I = A – P = Rs. 40625 – 32500 = Rs. 8125*

*= 5%*

*∴*

*Rate of interest is 5% per annum.*

*Example 3: In what time will the sum of money double itself at the rate of 10% per annum?*

*Solution:*

*Here,*

*P = Rs. x (let)*

*A = Rs. 2x (double of principal)*

*I = A – P = Rs. 2x – x = Rs. x*

*R = 10%*

*T = ?*

*We have,*

*= 10 years*

*∴*

*The required time is 10 years.*

*Example 4: Find the sum that will amount to Rs. 7500 in 5 years at the rate of 10% per annum simple interest.*

*Solution:*

*Here,*

*A = Rs. 7500*

*T = 5 years*

*R = 10%*

*P = ?*

*We have,*

*= Rs. 5000*

*∴*

*The required sum is Rs. 5000.*

*Example 5: Jenisha deposited Rs. 200,000 in two banks so that first bank and second bank offer 5% p.a. and 10% p.a. rate of interest. How much interest is received separately, if her total amount is Rs. 246,760 after 4 years?*

*Solution:*

*Here,*

*Total principal (P) = Rs. 200,000*

*Total amount (A) = Rs. 246,760*

*∴*

*Total interest (I) = A – P = Rs. 246,760 – 200,000 = Rs. 46,760*

__In first bank__,

*P = Rs. x (let)*

*T = 4 years*

*R = 5%*

__In second bank__

*,*

*P = Rs. 200,000 – x*

*T = 4 years*

*R = 10%*

*According to question,*

*I*_{1}+ I_{2}= Rs. 46760

*or, 8,000,000 – 20x = 4676000*

*or, - 20x = 4,676,000 – 8,000,000*

*or, -20x = -3,324,000*

*or, x = -3,324,000/-20*

*or, x = 166,200*

*∴*

*Interest from first bank (I*_{1}) = 20x/100 = 20×166200/100 = Rs. 33240

*∴*

*Interest from 2*^{nd}bank (I_{2}) = Rs. 46760 – 33240 = Rs. 13520

*You can comment your questions or problems regarding the simple interest here.*

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