**Which Debt Should Be Cleared off First?** **Simple Interest vs Compound Interest Loan**

Commercial Maths is a pivotal topic from a practical point of view. Commercial Maths is applied by all of us in daily life, right from buying vegetables from the shopkeeper to calculating our taxes. Some of the topics in Commercial Maths are as follows:

- Money
- Ratios
- Proportions
- Percentages
- Unitary Method
- Profit and Loss
- Simple Interest
- Compound Interest
- Taxes

As we realise the importance of these topics in our day to day life, we must understand them well and their applications.

Money is a very critical component to conduct our daily transactions.

In this article, we will be primarily focusing on the application of the concept of interest in loans and understand how interest can impact a loan and its structure. But before we discuss interest, let us first understand the concept of a loan.

A loan is a very comprehensive topic to understand. History has been witness to the fact that loans originated right from the time when our civilisation began to understand the need for doing business and transactions.

It all started with the ‘Barter system’ where we exchanged commodities in exchange for other commodities or services. As civilization progressed, we understood the need for a common and materialized **mode of payment** to maintain records, a system, and proper transactional transparency.

This need for transparency gave birth to the concept of ‘physical money’. After physical money was introduced into the system, the disparity among various classes in the society led to the accumulation of this ‘physical’ form of money by some classes while some classes ended up with the scarcity of wealth.

This is how the concept of a ‘loan’ came into existence.

**What is a loan?**

The concept of a loan can be explained in many ways, but to make it very easy to understand, it’s the lending of money to people or organisations, in exchange for an ‘interest’ in return along with the borrowed money.

Interest is simply the fee charged by the lender for providing the service of lending the money. Loan lending organisations are primarily responsible for lending this money by assessing the repayment capabilities of the loan purchaser.

Now, as the loan lending organisations lend money to the purchaser, there is a certain method by which the interest to be levied on the loan amount is calculated.

The interest on the loan is calculated by the bank depending on the tenure of the repayment period. Interest can be expressed in the form of a ‘percentage’, which is charged in addition to the amount borrowed from the bank by the lending institution.

Before we dive deeper into different types of interests that exist in the industry, let us understand a few basic terminologies that we will use while understanding interests.

**Principal Amount (P):**This is the amount which is initially borrowed from the bank or a lender by an individual. Interest is charged as a certain ‘percentage’ of the principal amount, which is subject to repayment in addition to the principal.**Rate of Interest (R):**As discussed above, it is the percentage of the principal amount charged by the bank, as a service charge for providing the loan to the borrower. Different banks and lenders charge different rates of interests.**Tenure of the Loan (N):**It is the time of the repayment period of the loan. Interest is charged by the bank on this time period of the loan.**Interest Tenure (T):**This is the time for which the interest is charged on the loan. This is considered while calculating ‘Compound Interest’.**Amount (A):**This is the total amount to be repaid to the bank, along with the principal amount and the interest.

Amount = Principal + Interest

**Types of Interests**

Various types of interests that exist in the banking industry, but two of them are the most commonly known types that are widely practised all over the world, known as Simple Interest and Compound Interest.

Before we try to understand both these topics in a better way, let us try to first understand the basic underlying principles based on which they work.

## Simple Vs Compound Interest

**1. Simple Interest:**

As the name suggests, this is the simplest type of interest that exists in the industry. Simple interest is also known as the ‘US Rule’. In a simple interest loan, the interest is charged only on the principal amount borrowed from the bank. Here, we use the formula given below to calculate the simple interest:

**Interest = (P x R x T) / 100**

Where,

P = Principal Amount

R = Rate of Interest

T = Periods(Time)

To understand simple interest better, let us consider the following situation:

A college student obtains a simple interest loan to pay his college tuition fee of one year, which costs INR 10,000, and the annual interest rate on loan is 10%. If the student repays the loan over three years, what is the amount of simple interest paid?

Here, we can find the interest easily by first identifying the information required to find out the interest.

P = INR 10,000/-

R = 10%

T = 3 years

Hence, we can now find out the simple interest charged by substituting the values in the above formula of simple interest, which comes out to be INR 3,000.

**2. Compound Interest:**

As we just saw how simple interest works, let us now try to understand how compound interest works.

Here, there is a slight change in how the interest is charged by the bank or the lending organisation. In a compound interest loan, the interest is not charged on the fixed principal amount which is borrowed.

For every subsequent year, the interest is calculated on the amount of the previous year. For example, if ‘A’ is the principal amount borrowed and ‘B’ is the interest charged on it for one year, then the new amount at the end of the year is ‘A+B’. Now, for the 2nd year, the interest will be charged on the new amount, i.e., ‘A+B’ and not ‘A’.

To understand the examples better, let us consider the above-mentioned example.

The formula for compound interest can be given as follows:

**P [(1 + r/n100)^{nt}]-P**

The formula for the final amount using compound interest can be given as:

**A = P [(1 + r / n100) ]^{nt}**

P = Principal amount

r = Rate of Interest

n = Number of times the interest is applied

t = Number of time periods applied

Now, if we substitute the same values in the above formula, it turns out that the answer, if compared to simple interest, is not only different but also larger in magnitude.

**Compound Interest Loan v/s Simple Interest Loan**

Now finally comes the question of which loan is considered to be better?

Let us try to analyse both cases carefully here. In the case of a simple interest loan, the interest is calculated on the principal amount on which the loan was borrowed. It doesn’t change annually, as the principal amount remains fixed here.

But when we talk about compound interest loans, things are slightly different.

To make it easier to understand, an **‘interest is charged on the interest’**. But, this interest is charged generally when payment has defaulted.

Hence, if the instalments are paid back to the bank on time, then there is practically no difference between a simple and a compound interest loan.

But if the individual defaults on the instalment payment, then interest is charged on the interest.

If multiple payments have defaulted, then the interest on them gets accumulated, which can then result in a higher final amount to be paid back to the bank.

In some countries, **banks and lending organisations are prohibited from incorporating compound interest**, whereas, in many banks across the world, compound interest is incorporated in the system.

Looking at the examples above, we can conclude that a compound interest loan is certainly not a viable option to keep active for a long time, and hence, it is advised that it should be cleared off as early as possible, without defaulting on any instalments, to the bank.

Topics like **loans, interest, and compounding **tell us the importance of understanding the concepts of commercial math and its applicability in the practical financial world. As the applicability of such topics is very relevant in daily life, these concepts must be understood systematically by **studying** more real-life examples so that it is easier to relate to and link them, resulting in a better grasping of the concept.