Simple Interest Definition, Formula, Tips & Solved Questions

Simple interest is a quick and easy method of determining the interest charged on a loan or principal amount. SI is defined by simply multiplying the given interest rate with the principal amount and the number of days together. The concept of SI is employed in most areas such as finance, banking, automobile, and so on. Through this article learn the concepts of SI, through the formula, and examples on how to calculate simple interest. S.I. comes under one of those highlighted topics that are most commonly asked in all competitive exams like SSC( CGL, CHSL, JE), SBI Clerk, and similar exams.

What is Simple Interest?

Simple Interest is a basic way to calculate the extra money you have to pay or earn when you borrow or invest money. It is called “simple” because the interest is calculated only on the original amount (called the principal), not on the interest added over time. The formula used is:
Simple Interest = (Principal × Rate × Time) ÷ 100

Let’s understand this with an example. Suppose Ram takes a loan from the bank to buy a vehicle. He agrees to repay the loan after a certain time. While paying it back, he not only returns the amount he borrowed but also some extra money. This extra money is the interest, and it depends on how much he borrowed (the principal), for how long (time), and at what rate the bank charged interest.

Simple Interest makes it easy to know how much total money is to be paid or received.

Simple Interest Formula 

S.I. in mathematics as read in the introduction is a method that is applied to calculate interest on the money/capital or funds. Let us step towards the formulas relating to the topic, as the formulas play a major role in the easy calculation. The formula for S.I. is:
Simple interest= (Principal × Rate × Time) / 100
OR

1. I. = (P × R × T) / 100

Here, are the meaning of the various terms;

SI	SI stands for Simple Interest.
P	P denotes the principal amount. The principal amount(P) is the initial amount invested or borrowed by an individual from the bank.
R	R is the interest rate in percentage. The rate at which the principal amount is given to somebody for a certain time stands for the rate of interest.
T	T specifies the time duration in years. The duration for which the principal amount is provided to someone denotes the time.

Also below are formulas for Principal, Rate, and Time

The formula of Principal if Interest, Rate, and Time are given:

P = (S.I × 100) / (R × T)

The formula of Rate if Interest, Principal, and Time are given:

R = (S.I × 100) / (P × T)

The formula of Time if Interest, Rate, and Principal are given:

T = (S.I × 100) / (P × R)

In the simple type of interest, the interest always applies to the original principal amount, with the same rate of interest for every time cycle. When we invest our money in any bank, the bank provides us with interest on our amount.

There is one more term called “Amount”, which is defined as the total money that is to be paid back at the end of the period for which it was borrowed. In general, when an individual takes a loan or borrows some money he/she has to repay the principal borrowed + the interest amount, and this complete quantity is known as the amount.

To calculate the amount;

Amount = Principal + Simple Interest= P + SI

Simple Interest Formula for Months

In the previous section, we read the formulas relating to S.I, principal, interest, rate and time duration. So far we discussed the S.I. calculation on a yearly basis. Let us learn more about the formulas relating to months in terms of 3, 4, 6, 9 months. In general;

S.I. = (P × R × T) / 100

Here T is for the number of years.

The formula for S.I. modifies to:

S.I. = (P × R × x) / (12 × 100)

Here x = Number of months

For example, if x = 4, that is for 4 months, the formula would be:

S.I. = (P × R × 4) / (12 × 100) = (P × R) / (3 × 100)

Similarly, for half-yearly, that is for 6 months:

S.I. = (P × R × 6) / (12 × 100) = (P × R) / (2 × 100)

Why is Simple Interest important?

As mentioned earlier, SI plays an important role in finance and is a simple and easy way to calculate interest. Si is also useful for short-term loans, enabling borrowers to estimate their repayment obligations accurately and predict their financial costs. Its transparency empowers borrowers to comprehend how interest accumulates over time, aiding in sound financial decision-making. Moreover, SI is a foundational concept for introductory financial education, with applications in various consumer loans and legal and regulatory contexts. However, it does not capture the complexities of transactions involving compounding interest or more sophisticated investment scenarios where other methods are more appropriate for precise assessments.

Types of Interest

Interest is the extra amount paid by a borrower to a lender for using money over time. There are mainly two types of interest: Simple Interest and Compound Interest.

Simple Interest is calculated only on the original amount (called the principal) for a fixed time and at a fixed rate. The formula is easy:
Simple Interest = (Principal × Rate × Time) / 100.
This type is commonly used for short-term loans or savings.

Compound Interest, on the other hand, is calculated on the principal amount plus the interest that has already been added. This means you earn or pay interest on interest over time. It’s commonly used in bank savings accounts, investments, and long-term loans.
The amount grows faster with compound interest compared to simple interest.

Apart from these, in advanced finance, there are other types like fixed interest, variable interest, and nominal interest, but for most basic calculations, knowing the difference between simple and compound interest is enough.

Understanding both types helps in making better financial decisions, especially when taking loans or investing money. It helps you know how much you'll earn or owe over time. 

How to Find Simple Interest 

Simple Interest is a way to find out how much extra money you have to pay or get for using someone else's money over time. It is calculated using a very easy formula:

Simple Interest (SI) = (P × R × T) / 100

Where:

• P = Principal (the amount of money borrowed or invested)
• R = Rate of interest per year
• T = Time in years

To find the simple interest, you just multiply the principal, rate, and time, and then divide the result by 100.

Example:
Michael’s father took a personal loan of $1,000 from the bank. The interest rate was 5% per year. Let’s find out how much interest he will pay for different time periods and the total amount to be returned.

Given:
Principal (P) = 1,000
Rate (R) = 5% per year

Now, let’s calculate the interest and total amount for different time periods:

Time (Years)	Simple Interest (SI)	Total Amount (A = P + SI)
1 Year	SI = (1000 × 5 × 1)/100 = 50	1000 + 50 = 1050
2 Years	SI = (1000 × 5 × 2)/100 = 100	1000 + 100 = 1100
3 Years	SI = (1000 × 5 × 3)/100 = 150	1000 + 150 = 1150
10 Years	SI = (1000 × 5 × 10)/100 = 500	1000 + 500 = 1500

Difference Between Simple Interest vs Compound Interest

What is the difference between simple and compound interest?

There are two types of interest: simple and compound interest. In this particular article, our focus was on S.I from all corners. Let us understand the difference between simple interest and compound interest.

Simple Interest vs Compound Interest

Simple Interest	Compound Interest
The S.I is computed on the original principal amount every time.	Compound interest, when compared to S.I, is determined on the collected sum of principal and interest.
The principal amount is constant in such a type of interest.	The principal amount is constantly varying during the complete borrowing period.
SI is calculated by the formula: S.I. = (P × R × T) / 100	CI is determined by the formula: C.I. = P(1 + R/100)^T – P   C.I stands for compound interest and is the total amount (including principal and interest) after a certain time period. P denotes the principal amount. R is the interest rate in percentage. T specifies the time duration in years.
The S.I. is identical for every year on a certain principle taken.	The compound interest varies per year for the span of the time as it is determined on the amount and not principal.
An amount if invested using S.I., gives a lesser return.	The same amount when invested using C.I. gives much higher returns.

Key Takeaways of Simple Interest

It is straightforward to calculate SI using the formula. Below are some of the takeaways regarding the topic:

• SI profits customers who repay their loans on time/ early each month.
• Auto loans and short-term individual loans are normally SI based loans.
• SI is estimated on the Principal Amount for the complete tenure.
• Principal Amount prevails constantly in SI.
• The amount of interest is always more for the case of compound interest when compared to simple interest.
• The earned interest on the given principal is not included to determine the interest for the next term.
• The collection of interest is slow in this approach.
• A simple type of interest is advantageous to the borrower when compared to the lender as a borrower will be spending slightly less on a loan that is taken on S.I.

Know more about Percentages

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Important Points About Simple Interest

• When the rate of interest is given as a percentage, we use the formula:
  Simple Interest = (P × R × T) / 100
• But if the rate is already in decimal form (like 0.05 instead of 5%), then you don’t need to divide by 100. Just use:
  Simple Interest = P × R × T
• The rate of interest means how much extra money you earn or pay on every $100 in a fixed time.
• Compound Interest always gives more return than Simple Interest if everything else (like amount, rate, and time) stays the same.
• The method used to find Compound Interest is based on the concept of Simple Interest.

Applications of Simple Interest 

Simple Interest is widely used in everyday financial situations like loans, savings, and investments. It helps calculate how much extra money is paid or earned over time on a fixed amount. Common uses include bank loans, fixed deposits, and installment payments.

1. Bank Loans:
   When people take loans from banks—for buying a home, car, or for education—the interest they have to pay is often calculated using simple interest. This helps them know how much extra money they need to repay over time.
2. Fixed Deposits (FDs):
   When you keep your money in a fixed deposit, the bank pays you interest on your savings. This interest is usually calculated using the simple interest formula, so you can easily find out how much you’ll earn by the end of the FD period.
3. Recurring Deposits (RDs):
   RDs allow you to save a fixed amount every month. At the end of the period, the bank pays interest—usually calculated with simple interest—on the total amount saved. This helps you know the final amount you will receive.
4. Installment Schemes:
   When you buy things like furniture or electronics on monthly installments, stores often add simple interest on the price. Knowing how simple interest works helps you figure out the total cost over the payment period.
5. Microfinance Loans:
   In small towns or villages, microfinance companies give small loans to people who can’t get bank loans. These loans usually charge simple interest. This makes it easier for borrowers to understand how much they need to repay.

Simple Interest Problems

Having a thorough knowledge of S.I. definition, formulas concerning yearly and monthly along with the knowledge of terms like principal, rate, interest, amount and time. Let us step towards some simple interest questions for better understanding.

Solved Question 1: Determine the Simple Interest (S.I.) for a principal amount of Rs. 4000, for 2 years at a rate of 20% per annum.

Solution:
Given:
Principal (P) = Rs. 4000
Rate (R) = 20%
Time (T) = 2 years

Using the formula:
S.I. = (P × R × T) / 100
S.I. = (4000 × 20 × 2) / 100
S.I. = 1600 rupees

We can also calculate the Simple Interest and Total Amount for the same principal and rate, but for different time durations:

Time (Years)	Calculation	Simple Interest (Rs.)	Amount (Rs.) = Principal + Interest
1	(4000 × 1 × 20) / 100 = 800	800	4800
2	(4000 × 2 × 20) / 100 = 1600	1600	5600
3	(4000 × 3 × 20) / 100 = 2400	2400	6400
5	(4000 × 5 × 20) / 100 = 4000	4000	8000
7	(4000 × 7 × 20) / 100 = 5600	5600	9600
9	(4000 × 9 × 20) / 100 = 7200	7200	11200
10	(4000 × 10 × 20) / 100 = 8000	8000	12000

Solved Question 2: Determine the simple interest for a given principal amount of Rs. 2000, the duration is 3 months and the rate of interest is 10%.

Solution:
Given terms

P = 2000
R = 10%
T = 3 months
SI = ?

Using the formula for SI:

S.I. = (P × R × x) / (12 × 100)
Here x = Number of months

S.I. = (2000 × 10 × 3) / (12 × 100)
⇒ 50

Solved Question 3: If the final amount on a certain amount of money becomes Rs. 720 in 2 years and Rs. 1020 in another 5 years in simple interest, then what is the annual rate of interest?

Solution: Formula used:

Where P = principal

R = rate of interest

T = time

Principal = Amount – Interest

Calculation:

Money become 720 in 2 years and becomes 1020 in another 5 years

⇒ Interest in 5 years = (1020 – 720) = 300

⇒ interest in 1 year = 300/5 = 60

⇒ Interest in 2 year = 60 × 2 = 120

We are given that money becomes Rs. 720 in 2 years

Principal = Amount – Interest

Principal = 720 – 120 = 600

Let, rate of interest = r%

Accordingly,

(600 × 2 × r)/100 =120

⇒ r = 10

∴ The rate of interest is 10%

Check about Probability here.

Solved Question 4: A sum of Rs. 4000 is lent on simple interest at the rate of 10% per annum. The S.I. for 5 years is how much more than the S.I. for 3 years?

Solution:
Given:

A sum of Rs. 4000 is lent on S.I. at the rate of 10% per annum

P = 4000
R = 10%

Formula used:
S.I. = (P × R × T) / 100

Calculation:

S.I. for 5 years = (4000 × 5 × 10) / 100 = 2000
S.I. for 3 years = (4000 × 3 × 10) / 100 = 1200

⇒ Difference between S.I. for 5 years and S.I. for 3 years = 2000 – 1200 = 800

∴ S.I. for 5 years is 800 more than S.I. for 3 years.

Here you can get more solved example Questions of Simple Interest.

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Simple Interest Questions and Answers

Q1. How do you calculate simple interest? How do you find simple interests? What is a simple interest loan?

Solution:

The formula to compute simple interest is as follows: SI = Principal (P) × Rate (R) × Time (T) / 100. Multiply the principal amount by the interest rate and the time (in years) to find simple interest, then divide the result by 100. In a loan with simple interest, interest is only computed on the original principal amount—no compounding is involved. It's straightforward, as the interest remains constant throughout the loan term. The formula helps determine the total interest earned or paid over time. Simple interest is commonly used in personal loans, car loans, and short-term financial transactions, offering a clear and easy-to-calculate method for interest accrual.

Q2. What is the formula for simple interest? How to do simple interest?

Solution:

The formula for simple interest is SI = P × R × T / 100, where SI = simple interest, P = principal amount, R = the interest rate per annum, and T = the time in years.
To calculate the simple interest (SI), multiply the principal amount by the interest rate and the time in years, and then divide it by 100.
For example, if you have a Rs. 1,000 principal, a 5% annual interest rate, and 2 years,
Then, the simple interest would be (1000 × 5 × 2) / 100 = Rs. 100. Simple interest provides a straightforward method for calculating interest without compounding.

Q3. How does simple interest work? How do you find principal in simple interest?

Solution:
Simple interest works by calculating interest solely on the initial principal amount without considering any previously earned interest. The formula is SI = P × R × T / 100, where SI is the simple interest, P is the principal, R is the interest rate, and T is the time in years. To find the principal in simple interest, rearrange the formula: P = SI × 100 / (R × T). This formula allows you to determine the original amount borrowed or invested when given the simple interest earned, interest rate, and time. Understanding simple interest helps in assessing the cost of borrowing or the return on investment in various financial scenarios.

Q4. Why is compound interest preferable to simple interest when investing?

Solution:
Compound interest is preferable to simple interest when investing because it allows for exponential growth of wealth over time. In compound interest, interest is earned not only on the initial principal but also on the previously accumulated interest. This compounding effect leads to the snowballing of returns, resulting in higher overall gains. As time progresses, compound interest accelerates wealth accumulation, making it a powerful tool for long-term investments. It leverages the concept of earning interest on interest, enabling investors to maximize returns and build substantial wealth. While simple interest provides a linear growth pattern, compound interest offers the potential for significant and sustained financial growth, making it a more effective strategy for investors with a long-term perspective.

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