What is the difference between simple interest and compound interest Class 8?

Difference between Simple Interest & Compound Interest Simple Interest In simple interest, interest for all years is same. SI is smaller than CI Formula is Interest = (𝑃 × 𝑅 × 𝑇)/100 Interest is on Principal amount only. Compound Interest In compound interest, interest for all years is different. CI is larger than SI Formula is Amount = P (1+𝑅/100)^𝑛 Interest is on previous interest as well as the principal amount.

The Major Difference Between Simple Interest and Compound Interest is just that Simple Interest is calculated on the Principal whereas Compound Interest is calculated on the Principal Amount along with the Interest accumulated for a certain period of time. Both Simple and Compound Interest are widely used concepts in the majority of financial services. Check out Solved Example Problems for finding the difference between CI and SI in the later sections. Get to know about the concept Difference of Compound Interest and Simple Interest in detail by going through the entire article.

How to find the Difference Between Simple Interest and Compound Interest?

Let us discuss in detail how to find the Difference between Simple Interest and Compound Interest. They are along the lines

Consider the Rate of Interest is the same for both Compound Interest and Simple Interest

Difference = Compound Interest for 2 years – Simple Interest for 2 Years

= P{(1+r/100)2-1} – P*r*2/100

= P*r/100*r/100

=((P*r/100)*r*1)/100

Solved Examples on Difference of Compound Interest and Simple Interest

1. Find the difference of the compound interest and simple interest on $ 10,000 at the same interest rate of 10 % per annum for 2 years?

Solution:

Simple Interest = PTR/100

= 10,000*10*2/100

= $2000

To find the Compound Interest firstly calculate the Amount

Amount A = P(1+R/100)n

A = 10,000(1+10/100)2

= 10,000(110/100)2

= 10,000(1.21)

= $12,100

Compound Interest = Amount – Principal

= 12,100 – 10,000

= $2,100

Difference between CI and SI = CI for 2 Years – SI for 2 Years

= $2100- $2000

= $100

2. What is the sum of money on which the difference between simple and compound interest in 2 years is $ 100 at the interest rate of 5% per annum?

For her investment, Ms Devika receives INR 21,000 at the end of three years (investment tenure). The bank or the financial institutions pays Ms Devika an interest of 7% for using her deposit amount for its operations during the tenure of her investment (three years). The INR 7,000 is the interest that Ms Devika receives on her deposit from the borrower.

The simple interest should be calculated according to the duration of the investment or loan. If a loan is only for a few days or months, the interest rate has to be converted into a daily or monthly basis. Let’s take an example of a loan that charges interest on a daily basis to understand it better. 

Example 2

The principal amount of a loan is INR 50,000, of tenure of 60 days, with an interest rate of 5% per annum. One can compute the simple interest, in this case, as follows.

Principal amount – INR 50,000

Tenure – 60 days

Interest rate – 5% per annum or 0.014% per day.

Simple interest = INR 410.95

Therefore, the total interest the borrower will pay for the INR 50,000 loan for a tenure of 60 days is INR 410.95.

It is important to note that the higher the amount, the higher will be the interest. Also, the higher the duration of the investments, the greater will be the interest.

What is Compound Interest?

Unlike simple interest, which gains interest only on the principal sum, compound interest (CI) earns interest on the previously earned interest. The interest is added to the principal amount. CI is simply Interest on Interest. The whole principle revolves around generating high returns by compounding the interest received on the principal sum. 

In other words, CI has the potential to earn more return than just the simple interest from an investment. The investments grow exponentially with compound interest because it is based on the principal power of compounding.

The bank or financial institution, or the lender decide on the frequency of compounding. It can be daily, monthly, quarterly, half-yearly or yearly. The higher the frequency of compounding, the higher will be the interest accrual amount. Hence, investors benefit from compound interest more than borrowers.

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.

What is the formula for compound interest?

CI is calculated by multiplying one plus interest raised to the power of the compounding periods with the principal amount. Finally, the principal amount has to be subtracted to obtain the CI.

One can use the following formula to calculate compound interest:

A=P(1+r/n)^(n*t)-1)

Where,

A – Compound Interest

P – Principal Amount

r – the rate of interest

n – the number of compounding periods

t – number of years (duration)

Example 1

Let’s understand CI calculation with an example. Mr Charan invests INR 10,000 at the rate of 10% for five years. One can compute the CI using the formula.

A = 10000*((1+10%)^(5)-1)

A = INR 6,105.

The interest earned by Mr Charan is INR 6,105. The corpus at the end of his investment tenure is INR 16,105 (the principal and the interest). On the other hand, the simple interest for the same investment and tenure is INR 5,000. The difference between SI and CI amount is INR 1,105.

Example 2

If the frequency of compounding is higher, then the interest will be higher. Also, if the investment duration is higher, the returns will be higher as well. Let’s take the same example as above but with higher compounding periods to understand how the interest will be higher in this case.

Investment – INR 10,000

Interest – 10% per annum

Tenure – 5 years

Compounded – half yearly, therefore the compounding periods are 2

A = 10000*((1+10%/2)^(5*2)-1)

A = 10000*((1+5%)^(10)-1)

The CI in this case, for Mr Charan is INR 6289. The corpus at the end of his investment tenure is INR 16,289 (the principal and the interest). Mr Charan earned INR 183 extra in this case. Hence with higher compounding periods, the interest will also be higher.

Also, one can use the Scripbox’s Compound Interest Calculator to determine the values faster.

Explore Best Banks in India

What is the power of compounding?

Compounding refers to a scenario where interest earns interest. It simply means when earnings are reinvested, the initial investment and the reinvested earnings grow at a constant rate. This makes the investments multiply at a faster rate. This is called the power of compounding. The higher the compounding frequency, the higher will be the returns from the investment. Compounding frequency is the number of times the interest is calculated in a year.

Compounding is a compelling concept, and no wonder Albert Einstein called it the 8th wonder of the world. Under compounding, you can make your money work harder for you. The interest that accumulates earns more interest in the long term. Also, the longer you stay invested, the higher will be the return from an investment. Hence it is advisable to start investing at early ages to benefit from the power of compounding.

What is the difference between compound and simple interest?

What is the difference between simple interest and compound interest for kids?

What is compound interest of Class 8?

What is the difference between compound interest and simple interest for 2 years?