Simple Interest

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 Formula

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

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...

When Time is given in Months

When the time is given in months instead of years, you just convert months into years in the formula.

T = Months/12

Then put this into the simple-interest formula: S.I. =\dfrac{P \times R \times T}{100}

Substituiting T = M/12:

S.I. =\dfrac{P \times R \times M}{100\times 12}

Similarly, when time is given in days, the formula becomes: S.I. =\dfrac{P \times R \times d}{100\times 365}

Terms Related to Simple Interest

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.

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+\frac{R \times T}{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.

Adam 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

The key differences between the two are highlighted in the table below:

Related Articles:

• Difference between Simple and Compound Interest.
• Simple Interest Quiz
• Shortcuts and Tricks for Simple Interest
• Applications of Simple Interest

Solved Questions on Simple Interest

Question 1: Sam takes a loan of $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 = $20000
• Rate of Interest per year = R = 10%
• Time (T) = 1 year

SI = (P × R ×T) / 100
= (20000 × 10 × 1) / 100 
= $2000
Total Amount that Rajesh has to pay to bank at end of year 

Amount = Principal + Simple Interest
= 20000 + 2000 
= $22,000

Question 2: A person borrowed $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 = $60,000
• Rate of Interest = 2.5 %
• Time = 4 years

SI = (P × R ×T) / 100 
= ( 60,000 × 2.5 × 4 ) / 100 
= $6000 

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

Solution:

• A = $8000
• P = $6000

Amount = Principal  + Simple Interest

SI = A – P 
= 8000 – 6000 
= $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 %.