Simple Interest (SI) is a method of calculating the interest charged or earned on a principal amount over a fixed period. It is calculated based solely on the principal amount, which remains unchanged throughout the calculation.
Simple Interest is widely used across industries such as banking, finance, and automotive sectors to determine interest on loans, investments, and financing options. This straightforward method enables consumers and businesses to easily understand the cost of borrowing or the returns on their investments.
Simple interest is fundamentally based on arithmetic progression.
In simple interest, the interest grows linearly over time. This means the amount of interest added each year is the same, forming a sequence in arithmetic progression (AP).
For example:
- If the principal is ₹100, the rate is 10%, and the time is in years, the interest added each year will be ₹10.
- After 1 year: ₹10
- After 2 years: ₹20
- After 3 years: ₹30
- And so on...
The formula to calculate Simple Interest is:
Where,
- P is the Principal amount
- R is annual Rate of Interest
- T is the Time for which principal is invested
Three basic terms related to simple interest are:
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 increases after every cycle.
It can be calculated as:
P =\dfrac{100 \times S.I.}{R \times T}
Rate
The rate of interest at which the principal amount is invested or borrowed for a specific period, 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".
It can be calculated as:
R =\dfrac{100 \times S.I.}{P \times T}
Time
The duration during which the principal is borrowed or invested is referred to as time. Time is symbolized by "T".
It can be calculated as:
T =\dfrac{100 \times S.I.}{P \times R}
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)
Simple Interest Calculator
Use this calculator to quickly calculate both the simple interest and the total amount.
How to Calculate Simple Interest
To understand the concept better, let's try finding the simple interest using an example.
Ravi deposits ₹8,000 in a savings account at a simple interest rate of 7% per annum for 3 years. What will be the simple interest earned, and what will be the total amount after 3 years?
Solution:
- P = ₹8,000
- R = 7% per annum
- T = 3 years
SI = (P × R × T/100)
SI = 8000 × 7 × 3 / 100
SI = 168000/100 = 1680
Total Amount = Principal + Interest
Total Amount = 8000 + 1680 = ₹9680
Steps to Find Simple Interest
Simple interest is found by using the formula SI = (PRT)/100. 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 loan amount is noted.
Step 2: Use the formula SI = (P×R×T/100) to calculate 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 required simple interest.
Let's consider an example to understand the procedure better.
Example: Find the SI on ₹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 ₹1,500
Simple Interest vs Compound Interest
Simple interest and compound interest are two common methods used to calculate the interest on a loan or investment. While both serve the same purpose—to determine how much extra money is paid or earned—compound interest is often considered more complex due to its method of calculation.
The key differences between the two are highlighted in the table below:
Simple Interest vs. Compound Interest |
|---|
Simple Interest | Compound Interest |
|---|
| Simple interest is calculated on the original principal amount. | Compound interest is calculated on the accumulated sum
of principal and interest. |
Simple Interest can be calculated using the following formula: SI = P × R × T | Compound Interest can be calculated using the following formula: CI = P [(1 +R/100)T - 1] |
| The principal remains constant throughout the tenure. | The principal amount changes every year during the tenure. |
| It is equal for every year on a certain principle. | It is different for every span of the time period, as it is
calculated on the amount and not the principal. |
Read More: Difference between Simple and Compound Interest.
Applications of Simple Interest
The following are the five most popular real-life applications of simple interest:
- Bank Loans: Many individuals in India take out loans from banks for various purposes such as buying a house, a car, or funding education. Banks typically calculate the interest on these loans using simple interest. Borrowers need to understand how much interest they will be paying over the loan term.
- Fixed Deposits: When individuals invest their money in fixed deposits, banks pay them interest on the principal amount deposited. The interest earned is usually calculated using simple interest. Investors can use simple interest calculations to determine their returns over the FD tenure.
- Recurring Deposits: Similar to fixed deposits, recurring deposits (RDs) allow individuals to save money over a period of time. The interest earned on recurring deposits is also calculated using simple interest. Customers can calculate the maturity amount they will receive at the end of the RD tenure based on the monthly deposit and the applicable interest rate.
- Retail Installment Schemes: Many retail stores and businesses offer installment schemes for purchasing goods such as electronics, furniture, or appliances. These schemes often charge simple interest on installment payments. Customers can understand the total amount they will pay over the installment period by calculating the simple interest component.
- Microfinance: In rural areas and small towns of India, microfinance institutions provide financial services to low-income individuals and entrepreneurs who may not have access to traditional banking services. The interest charged on microfinance loans is typically calculated using simple interest. Borrowers can determine the total repayment amount based on the principal borrowed and the applicable interest rate.
Solved Questions on Simple Interest
Question 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 bank at end of year
Amount = Principal + Simple Interest
= 20000 + 2000
= Rs 22,000
Question 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
Question 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:
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, rate of interest R is 11.11 %.
Practice Quiz: Simple Interest Quiz
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