# Simple Interest

## 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.

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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.

### 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

### 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,
I1 + I2 = 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 (I1) = 20x/100 = 20×166200/100 = Rs. 33240
Interest from 2nd bank (I2) = Rs. 46760 – 33240 = Rs. 13520

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