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When you deposit some amount in bank or lend some amount to other, you will get extra dollar in given amount. This is called interest. Here, we talk about simple interest. As the name suggests, it is very easy to calculate simple interest. You have to remember only one basic formula which I will explain that in detail. The formula is


http://quicklatex.com/cache3/7e/ql_900c5e151b96206394206ed55ff6c77e_l3.png


![Screenshot (130).png](https://steemitimages.com/DQmX8PtE4PQ7quijddG7ijBTBg5QjTUw8DWfav5AH1CrY6W/Screenshot%20(130).png)

![Screenshot (127).png](https://steemitimages.com/DQmXsTKiGJAA5FjSMNrW3wSrbBZTgBMFiM6MpKJD6tKptFk/Screenshot%20(127).png)

![Screenshot (128).png](https://steemitimages.com/DQmdMsXtSNQnAhm6yptgAKEZFezhwdHTiZCntZmQZSCo3q4/Screenshot%20(128).png)

![Screenshot (129).png](https://steemitimages.com/DQmZ8MMSrNsujL82n6Xce2v2rFGkNwoXdLnyuDZpS1udBmg/Screenshot%20(129).png)


A = Amount
It is total amount you get at end. It is also called as sum.

So, 

A = P + SI


<hr>

**Example 1: Simple Example**

You invest $100 at a 4% annual rate for 1 year. Find simple interest and sum. 

Solution:

First point out which information are given. $100 is amount you invested initially. So, it is principle(P). Rate is 4% and time is 1 year.

So, 

http://quicklatex.com/cache3/7e/ql_900c5e151b96206394206ed55ff6c77e_l3.png


http://quicklatex.com/cache3/4e/ql_5affbd4519c0b3ec06a96b02265faa4e_l3.png

http://quicklatex.com/cache3/c1/ql_97d7c9518b689261e4f73217c0484bc1_l3.png


Amount = P + SI = 100 +4 = 104 $


<hr>

**Example 2: When Interest is given**

You deposit some money into a bank account paying 4% simple interest per year. You received $30 in interest after 18 months. How much the deposit  was?

Solution:

Rate is given as 4%

Interest is $ 30 

Time = 18 months 

We have to find how much money was deposited i.e. principle. 

First convert time into years. 

http://quicklatex.com/cache3/52/ql_77e61bae0d00c5f335dd776af6b4d052_l3.png

Then, using same formula;

http://quicklatex.com/cache3/7e/ql_900c5e151b96206394206ed55ff6c77e_l3.png


or, http://quicklatex.com/cache3/4d/ql_78e3c2c0dd6bdd140cf7158cb193814d_l3.png

or, 30 * 100 = P * 6

or, 3000 = P * 6

or, P = 3000/6 

or, P = 500  $

In same way, rate and time can be found out when other variables are given.

<hr>

**Example 3: Profit of Bank**

Rina deposited 400 $ to bank at 5 % per annum for 2 years. Ram take a loan of same amount for same year but at 10 % per annum. How much [profit bank makes from these transactions. 

Solution:

For Rina:

Principle(P) = 400 $
Rate(R) = 5%
Time(T) = 2 years 

Simple interest(SI) = PTR/100

= 400*2*5/100

= 40 $

For Ram:

Principle(P) = 400 $
Rate(R) = 10%
Time(T) = 2 years 

Simple interest(SI) = PTR/100

= 400*2*10/100

= 80 $

Interest given to Rina by Bank = 40 $
Interest taken by Bank from Ram = 80 $

Profit made by bank = 80-40 = 40 $


<hr>

**Sources**


i. [Questions](https://www.indiabix.com/aptitude/simple-interest/)