Simple Interest

Imagine lending a certain sum of money to your friend or family, and in return, they pay you an extra amount to show their appreciation towards you for letting them borrow the sum. This additional amount is the interest, which we call simple interest when calculated using a fixed rate of percentage of the original amount. This concept is one of the most crucial topics in mathematics and finance. 

In this guide, we will break down how simple interest works, teach you how to calculate it with simple formulas and show you how it compares to compound interest.

1.0Understanding Simple Interest

Simple Interest is a method of calculating interest, where it is calculated on only the initial amount (referred to as the principal) and does not consider any interest already incurred. It is one of the simplest methods to calculate interest and is widely used in personal loans, savings accounts, and fixed deposits. 

The interest for simple interest calculation remains constant for each period. For instance, imagine you are getting Rs 50 as interest for a certain sum after 1st year of investment, then after 10 years, you will still get Rs 50 as interest if the principal and rate remain the same. 

The major benefit of simple interest is the fact that it's straightforward to comprehend and use and suited for short-term money calculations.

2.0Simple Interest Formula

The simple interest formula is applied to calculate the amount of interest one would pay on an amount of money over a given time at a set interest rate. Mathematically, the formula for calculating the simple interest can be expressed as: 

$\text{Simple Interest (SI)}=\frac{P\times R\times T}{100}$

Here, 

• P (Principal): The starting amount of money that is being borrowed or invested. It is the original sum on which the interest is being calculated.
• R (Rate of Interest): The rate at which the interest is being charged or earned per period of time (usually per year). It indicates how much interest you will be earning or will owe on the principal annually.
• T (Time): The time period for which the money is borrowed or invested. It is normally in years but can also be in months, days, half-yearly, or quarterly, depending upon the problem. 

In banks, for larger and quicker calculations, the Simple Interest Calculator is usually employed to calculate the interest on loans or deposits quickly so that financial transactions can be processed with precision and accuracy. 

3.0The Equation for Simple Interest

The simple interest formula is not only used to determine the simple interest but can also be used to find values for other variables in the formula. In this section, we will be re-arranging the equation for simple interest to find these variables. Like this:

• Formula for the Principal in Simple Interest: The initial amount borrowed, lent, or invested can be calculated using the simple interest formula like this: 

$\text{Principal(P)}=\frac{SI\times 100}{R\times T}$

• Formula for the time in Simple Interest: The time period for which the sum is borrowed, lent, or invested can be calculated as: 

$\text{Time(T)}=\frac{SI\times 100}{R\times P}$

• Formula for rate in Simple Interest: The rate percentage for a certain sum can be calculated using the following formula for rate in Simple Interest:

$\text{Rate(R)}=\frac{SI\times 100}{T\times P}$

For a larger sum, the advanced Interest Calculator for Simple Interest can also be used to calculate these variables. These calculators efficiently calculate the other components of simple interest in addition to simple interest itself. 

4.0Difference Between Simple Interest and Compound Interest

Although Simple Interest (SI) is the simplest way to compute interest for short-term, for long-term calculation of interest, complex methods like Compound Interest (CI) are used. The most significant difference is how the interest is computed over time. Here are some other major differences between Simple Interest and Compound Interest: 

5.0Solved Problems of Simple Interest

Problem 1: A person invests Rs 1,500 at an interest rate of 5% per annum for 3 years. Calculate the simple interest earned on this investment.

Solution: Given that: 

Principal (P) = Rs 1500

Rate (R) = 5%

Time (T) = 3 years 

$\text{Simple Interest (SI)}=\frac{P\times R\times T}{100}$

$SI=\frac{1500\times 5\times 3}{100}$

$SI=Rs225$

Problem 2: An amount doubles itself in 5 years at simple interest. Find the rate of interest per annum.

Solution: Given that, Time (T) = 5 years 

Now, according to the question, in the given time frame: 

Amount(A) = 2(Principle) 

We know: $A=SI+P$

Hence, $SI+P=2P$

$SI=P$

Now, using the formula to calculate the SI: 

$\text{Simple Interest (SI)}=\frac{P\times R\times T}{100}$

$P=\frac{P\times R\times 5}{100}$

$1=\frac{R}{20}$

R = 20%

Hence, the rate of interest for the given investment is 20%. 

Problem 3: A sum amounts to Rs 8,400 in 3 years and Rs 9,600 in 5 years at simple interest. Find the principal and the rate of interest.

Solution: According to the question, 

Interest for 2 years = Rs 9,600 – Rs 8,400 = Rs 1,200

So, SI for 2 years = Rs 1,200

SI for 1 year = Rs 1200/2 = Rs 600

SI for 3 years = Rs 600 × 3 = Rs 1,800

Therefore, Principal = Rs 8,400 – Rs 1,800 = Rs 6,600

Now, using the formula of Simple interest: 

$\text{Simple Interest (SI)}=\frac{P\times R\times T}{100}$

$1800=\frac{6600\times R\times 3}{100}$

$1800=66\times R\times 3$

$R=\frac{600}{66}=9.06$

Hence, the rate of interest for the given investment is 9.06%.