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# Simple Interest

Simple Interest is the interest paid on the principal amount for which the interest earned on a regular basis is not added to the principal amount as we do in compound interest. Suppose we invest 100 rupees for 2 years at a rate of 10% for both simple interest and compound interest. Then for simple interest, the interest is calculated for 10% of 100 for the first year and similarly 10% of 100 for the second year. Now for compound interest for the first year, the interest earned is the same 10% of 100 but for the second year, we take into account the interest earned in the previous year i.e. the interest earned in the second year is 10% of (100 + 10% of 100). Thus we see that generally for the same terms compound interest is generally greater than simple interest.

## What is Simple Interest?

Simple Interse is the method to calculate the interest where we only take the principal amount each time without changing it with respect to the interest earned in the previous cycle. In simple terms, we can say that simple interest is the interest earned only because of the principal amount whereas compound interest is the interest earned on both principal and the previous interest earned.

Various investments and loans provided by banks and other financial sectors generally prefer compound interest. So one might ask what is the use of simple interest? This is generally used by low-income people who take small loans in the unorganised sector for a shorter duration of time i.e. for a few days to a few months.

The formula used to calculate the simple interest is shown in the image below, ## Notations in Simple Interest Formula

Various notations which are used in Simple Interest formulas are,

## Simple Interest Formula

Simple interest is a quick and straightforward method to calculate interest on the principal value. In the simple interest method, interest is always applied to the original principal amount, with the same rate of interest for each time cycle. When we put our money in a bank, we get interested in it. Banks charge a variety of interest rates, one of which is simple interest. The formula to calculate Simple Interest is,

S.I = (P × R × T )/100

Where,

• P is the Principal amount,
• R is anuall Rate of Interest, and
• T is the Time for which principal is invested.

### Principal

The principal is the amount borrowed or invested. It is denoted by the letter “P”. The principal remains constant while calculating simple interest whereas in compound interest the principal increase after every cycle.

### Rate

The rate of interest at which the principal amount is invested or borrowed for a specific period of time is called the rate. For Example, the rate of interest can be 5%, 10%, or 13%. Here the interest rate can be represented by “R”.

### Time

The duration during which the principal is borrowed or invested is referred to as time.  Time is symbolized by “T”.

### Amount

When a person acquires a loan from a bank, he or she is required to repay the principal borrowed plus the interest amount and the total amount repaid is referred to as the Amount. It is denoted by the letter “A”.

Thus,

• A = P + SI
• P = A – SI
• A = P(1 + RT/100)

## How to Find Simple Interest?

The simple interest on any sum of money is calculated using the steps discussed below,

Step 1: The Principal(P), Rate of interest(R) and time(T) of the loan amount is noted.

Step 2: Use  the formula SI = (P×R×T/100) to calculate the Simple Interest

Step 3: Use all the values from Step 1 and substitute them in Step 2.

Step 4: Simplify the value obtained in Step 3 to get the required simple interest.

Let’s consider an example to understand the procedure better.

Example: Find the SI on rupees 10000 deposited for 3 years at 5% per annum.

Solution:

Given,

P = Rupees 10,000
R = 5% per annum
T = 3 years

Thus, SI = (P×R×T/100)

⇒ SI = (10000×5×3)/100 = 1500

Thus the interest earn is rupees 1,500

### What Types of Loans Use Simple Interest?

Generally, all banks, financial institutions, and other money-lending companies apply compound interest on the loans as in this way they will earn will more interest from the customers. The calculations of compound interest are difficult and require a lot of calculation which is difficult for the common people to do.

So the loan disperses in the informal sector for a shorter period of time and is generally given on simple interest. For example, if a farmer wants to have a loan of 20,000 rupees for 3 months to prepare his crops he will go to a money lender who will give him the money at 3%-5% monthly interest. Here to make the calculations simpler these money lenders generally charge simple interest but at higher rates.

## Simple Interest vs Compound Interest

Simple interest and compound interest are two ways to calculate interest on a loan amount. It is believed that compound interest is more difficult to calculate than simple interest because of some basic differences between both. Let’s understand the difference between simple interest and compound interest through the table given below:

## Solved Examples on Simple Interest

Example 1: Rajesh takes a loan of Rs 20000 from a bank for a period of 1 year. The rate of interest is 10% per annum. Find the simple interest and the total amount he has to pay at the end of a year.

Solution:

Here,

Loan Sum = P = Rs 20000
Rate of Interest per year = R = 10%
Time (T) = 1 year

SI = (P × R ×T) / 100

= (20000 × 10 ×1) / 100
= Rs 2000

Total Amount that Rajesh has to pay to the bank at the end of the year

Amount = Principal + Simple Interest

= 20000 + 2000
= Rs 22,000

Example 2: A person borrowed Rs 60,000 for 4 years at the rate of 2.5% per annum. Find the interest accumulated at the end of 4 years.

Solution:

Given,

Principal = Rs 60,000
Rate of Interest = 2.5 %
Time  = 4 years

SI = (P × R ×T) / 100

= ( 60,000 × 2.5 × 4 ) / 100
= Rs 6000

Example 3: A person pays Rs 8000 as an amount on the sum of Rs 6000 that he had borrowed for 3 years. What will be the rate of interest?

Solution:

A = Rs 8000
P = Rs 6000

Amount = Principal  + Simple Interest

SI = A – P

= 8000 – 6000
= Rs 2000

Time (t) = 3 years
Rate (R) = ?

SI = (P × R ×T) / 100

R = (SI ×100) /(P× T)

R = (2000 × 100 /(6000 × 3)
= 11.11 %

Thus, the rate of interest R is 11.11 %

Example 4: If the principal is Rs 50,000, and the rate of interest is 10% per annum for a period of 4 years. What will be the total amount?

Solution:

Given

Principal = Rs 50000
Rate of Interest (r) = 10 %
Time period (t) = 4

Amount = Principal + Simple Interest

= P + PRT
= P(1 + RT)

= 50000 {1 + (10/100) × 4}
= 50000 {1+ 40/100}
= 50000 × 140/100
= 70000

Total amount will be Rs 70000.

Example 5: If the principal amount is Rs 5000 and the time is 2 years and the simple interest is Rs 4000 what will be the rate of interest?

Solution:

Given

Principal = Rs 5000
Time = 2
Simple Interest = 4000

SI = (P × R × T) / 100

4000 = (5000 × R × 2) /100

4000 = (10000/100) × R

(4000 × 100) / 10000 = R

R = 400000/10000
R = 40 %

Thus, the Rate of Interest is 40 %.

## FAQs on Simple Interest

### Q1: Define Simple Interest.

The type of interest that is levied only on the principal amount and not on the aggregated interest amount is called simple interest. While calculating simple interest we do not add interest earned in the previous cycle to the amount in the next cycle.

### Q2: What are Simple Interest formulas?

The formula to calculate the Simple Interest is,

SI = (P×R×T)/100

Where,

• P is the Principal amount,
• R is anuall Rate of Interest, and
• T is the Time for which principal is invested.

### Q3: What are Compound Interest formulas?

The formula to calculate the Compound Interest is,

C.I. = A – P

Where,

• A is the Amount i.e., A = P(1 + R/100)n , and
• P is the principal amount.

### Q4: Are Home Loans Simple or Compound Interest?

Usually, all the loans given by financial institutions are compound interest. So home loans are generally of compound interest type.