Simple Interest and Compound Interest

Simple Interest and Compound Interest is a crucial part of the Mathematics syllabus in a student’s middle school. Its necessity does not just end with the school exams. Still, a strong conceptual foundation benefits the students in various walks of life anytime he has to handle situations about financial settlements in future.

In this article, we will understand how the two are different, the formulas for both and in which situations will they apply.

Applications of Simple Interest and Compound Interest

Ram has borrowed Rs. 20,000 from Shyam for 5 years at 3% rate of interest. Find the amount Ram will have to pay Shyam at the end of 5 years. It is very common for us to come across scenarios where we happen to have borrowed money from our friends in times of necessity. Those familiar with banking transactions have heard our parents talk about having taken a loan from the bank in some interest that they have to repay after a certain period of time. Today in this article, we will find out how the calculation of interest-related sums is done.

In the above example mentioned, the Principal is Rs. 20,000. Let us find the interest that Ram has to pay after 5 years at 3% rate of interest. Simple Interest for Ram will be calculated by the below formula:

Simple Interest (SI) = Principal (P) * Time (T)* Rate (R) /100

SI = 20,000*5*3/100 = 3000

The Amount payable by Ram is calculated by adding the Simple Interest and Principal. Therefore, A = P + SI => A = Rs (20,000 +3000) = Rs. 23,000

Is this the only manner in which interest is calculated? No. The above sum is an example of Simple Interest. Suppose you have been told that the population of your town increases at the rate of 2% every year. At present, there are 600000 people in your town. You have been asked to calculate the population of your town at the end of 2 years. Will you apply the same method to find this out? No, in this situation, we will apply Compound Interest to arrive at the solution.

In this case, the Amount (Population) will be calculated with the following formula:

Amount = Principal (1+Rate/100)ⁿ

Therefore, at the end of 3 years, the population of a town will be calculated as:

Principal (1+Rate/100)ⁿ => 600000 (1+2/100)² = 6,24,240

Now let us take another example. You have deposited Rs. 30,0000 in a scheme. You will get 6% interest on the deposit amount, compounded monthly. Therefore, how much amount do you expect to withdraw after 20 years if the interest is compounded on a monthly basis?

Note the 6% rate is compounded on a monthly basis and not yearly. Therefore, in this case, the amount will be calculated as:

30,000 (1+6/100*12)^20*12= 30,000 (1+ 0.06/12)^20*12 = 9930.61

Difference Between Simple and Compound Interest

Until here, we have learnt:

The formula of Simple Interest and Compound Interest
How is the calculation of Simple Interest different from Compound Interest.
In which situation will we apply Simple Interest, and in which situation will Compound Interest be applicable.

Now, let us understand how Simple Interest is different from Compound Interest.

Simple Interest	Compound Interest
When we borrow a sum of money, and we have to pay back this amount after a certain period of time at a certain rate of interest, Simple Interest is applied	When the principal amount exceeds the due date for payment along with the rate of interest, for a certain duration, compound interest is applicable.
The amount is calculated on a constant principal	The interest of the previous year gets added to the principal every year.
The amount is constant and lesser	The amount is variable and higher
Growth is constant	Growth is rapid and higher

Who Is Benefited?

Compound Interest benefits the seller as he gets a higher return. On the other hand, since the return from Simple Interest is comparatively lesser, Simple Interest benefits the buyer more.

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