Interest is defined as payment from the borrower to the lender above the actual price of the loan taken, as compensation for the use of money, or for the delay in repayment. Conversely, interest can also be considered as the rate paid for money put on deposit. Economically speaking, one feasible explanation for the application of interest rates is to acquire a valid source of income for predominantly money-lending institutions and to avoid the scarcity of loanable funds. As a student of finances, or someone learning how to budget and handle money, it is essential to understand the concepts of Simple Vs Compounding Interest.
There are two ways interest on a principal amount can be calculated, simple interest and compound interest. Both methods are explained and compared in detail below.
Simple Interest
Explanation
Simple Interest is a fee that is calculated only on the original principal amount, irrespective of the tenure of the loan. Since simple interest does not increase over time, you know how much additional amount you will have to repay, before the start of the tenure itself. It is typically applied on loans about credit cards, education, mortgages, and personal loans, as it can be conveniently applied to time periods other than a year.
Formula
The formula to calculate simple interest is as follows:
R * P * N
Where ‘R’ is the rate of interest given by ‘pcpa’ or per cent per annum;
‘P’ is the principal amount borrowed at the beginning of the tenure. (INR or any form of currency);
‘N’ is the term of the loan, usually considered in years or months.
As is evident, we only need to find the product of the three attributes involved in order to obtain the simple interest.
In a varying form of the above-mentioned formula, we examine a slightly modified version to consider the cases where the term of the loan isn’t exactly annual. Then, we calculate it as follows:
R * P * NF
Where ‘R’ is the rate of interest (pcpa).
‘P’ is the principal amount. (INR or any form of currency).
‘N’ is the number of time periods elapsed.
‘F’ is the frequency of applying interest.
As aforementioned, the latter formula is used to calculate the interest when the term is in the form of months or weeks. The application of these formulae will be more comprehensible with the help of examples.
Examples | Simple vs. Compounding Interest
To understand the first simpler formula, consider this case. Assuming that a firm offers loans at a rate of interest of 8.56% per annum, a man borrows a principal of INR 12,000 for a term of 5 years. Therefore, according to the data, we can note that:
P = INR 12,000,
R = 8.56% per annum,
N=5 years.
Simple Interest = R * P * N
= 0.0856 * 12000 * 5
= 5136
Hence, the interest on the original amount is INR 5,136. The total amount to be repaid is the sum of the interest and the principal. That is 12,000 + 5,136 = INR 17,136.
Consider another example. Assume that a credit card holder has a balance of 5,000 and the rate of interest is given at 11.89% per annum; however, it is applied monthly. This way, the frequency of applying the rate of interest is 12 months. From the data, we conclude that over the course of one month, the attributes would look as follows:
P = INR 5,000,
R = 11.89% per annum,
N = 1,
F = 12 months,
Simple Interest = R * P * NF
= 0.1189 * 5000 * 112
= 49.54
Hence, after a month, the credit card holder would have to pay a total amount of
5,000 + 49.54 = INR 5,049.54.
Similarly, over the course of, say, six months, the attributes would look like:
P = INR 5,000,
R = 11.89% per annum,
N = 6,
F = 12 months,
Simple Interest = R * P * NF
= 0.1189 * 5000 * 612
= 297.25
This means that the net payable amount after 6 months would be:
5,000 + 297.25 = INR 5,297.25.
Compound Interest
Explanation
While understanding the concept of simple vs compounding interest, it is important to comprehend the way these interest amounts accumulate over time. Compound interest is the sum of interest to the principal amount borrowed. In other words, while calculating compound interest, we consider the interest applied initially while obtaining the newer interest. Because of this pattern, compound interest increases rapidly over time as compared to simple interest. It is often applied to boost long-term investment returns.
Formula
The total value to be calculated is given by:
F = P( 1 + RN )N*T
Where ‘F’ is the final amount (INR or any form of currency);
‘P’ is the original principal amount (INR or any form of currency);
‘R’ is the rate of interest (pcpa);
‘N’ is the frequency of compounding;
‘T’ is the total term (usually considered in years or months).
Now, to calculate the total compound interest, we must subtract the original principal amount from the final amount obtained by applying the above formula.
Therefore, compound interest will be given by:
Compound Interest = P( 1 + RN )N*T – P
The application and use of this formula will be more coherent after understanding examples.
Examples | Simple vs. Compounding Interest
Consider a principal amount of INR 45,000 deposited in a bank that pays a rate of interest of 6.12% per annum and is compounded every four months. Also, assume the total term is given to be 10 years. According to the data we have, we can conclude that:
P = INR 45,000,
R = 6.12% per annum,
N = 4 months,
T = 10 years.
Compound interest can be easily computed by means of the formula. However, we calculate the final amount first.
Final amount F = P( 1 + RN )N*T
= 45000 ( 1 + 0.06124 ) 4*10
= 45000 * 1.83558
= 82,601.505
To obtain compound interest, we subtract the principal amount from the final obtained amount.
Therefore, compound interest = 82601.52 – 45000 = INR 37601.505
Hence, compound interest is found to be INR 37,601.505.
Simple Vs Compound Interest: Differences
What differentiates simple vs compound interest is that after plotting the graphs of their growth on the basis of the same attributes, compound interest follows an exponential path, as opposed to the simple interest which grows linearly. Because of this, its growth is tremendously fast, which means the amount owed will also increase by following the same pattern. This is because compound interest is calculated on the principal amount and the accumulated interest, while simple interest is steadily obtained on the original principal amount only, irrespective of the interest applied over the tenure.
Here is a table that summarises the major differences between simple vs compounding interest, at a quick glance.
| Sr. No. | Parameters of comparison | Simple interest | Compound interest |
| 1. | Definition | Fee paid for using the borrowed money for a fixed period of time. | Fee levied on both borrowed money and the previously earned interest. |
| 2. | Interest to be obtained from | Principal amount | Sum of principal amount and previous interest. |
| 3. | Formula | R * P * NR * P * NF | P( 1 + RN )N*T – P |
| 4. | Behaviour on graph | Linear | Exponential |
| 5. | Returns | Lesser returns comparatively | Higher returns comparatively |
| 6. | Change in principal amount | There is no change in principal amount | Principal amount increases as interest gets compounded |
Applications of Simple vs. Compounding Interest
Compound Interest is used widely to calculate the returns over longer periods of time for stocks, mutual funds, and investment portfolios. They are also usually used in bank accounts. Simple Interest is more often applied to simpler loans like credit cards, student loans, consumer loans, or mortgages. Although these are the general applications of both simple vs compounding interest, there is no actual guarantee that all financial institutions would use the same. It differs from company to company and depends solely on the rules and regulations of that particular establishment. Hence, it is essential to keep your eyes peeled while taking big financial decisions, especially concerning loans.
Comprehending the differences between simple vs compound interest is essential to help take control of our own finances. In any situation, where lending and borrowing of money are involved, interest rates are bound to appear. This makes it important for each of us to learn the applications of simple and compound interest inside out to avoid getting spammed.
FAQs related to Simple vs. Compounding Interest
Q1. What is the difference between simple and compound interest?
Ans: Simple interest is calculated on the original amount of a loan. Compound interest is calculated on the principal amount and the accumulated interest of previous periods, and thus can be regarded as “interest on interest.”
Q2. Why is compound interest better than simple?
Ans: When it comes to investing, compound interest is better since it allows funds to grow at a faster rate than they would in an account with a simple interest rate.
Q3. Do banks use compound or simple interest?
Ans: Banks use compound interest for some loans. But compound interest is most commonly used in investments. Also, compound interest is used by fixed deposits, mutual funds, and any other investment that has reinvestment of profits.
Q4. What are the disadvantages of compound interest?
Ans: Compound interest is advantageous only over the long term, and works in your favour when the tenure is long. In case you’re borrowing money from an institution that applies compound interest, it could significantly increase the financial burden over time.
Q5. Are student loans compound or simple?
Ans: All federal student loans and most private student loans charge simple interest instead of compound interest. With simple interest, you pay interest only on your principal amount and don’t acquire interest on your unpaid interest. Because of this, you pay comparatively less interest over the life of your loan.
Thank you for reading this guide to simple vs compound interest! Let us know if you have any queries, in the comment section below.
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