Application of Simple Interest: In our daily lives, sometimes, we come across a situation where we need to borrow money from a bank, post office or a moneylender for a specified period. At the end of this period, we must pay back the money we had borrowed plus some additional money for using the lender’s money. This additional money is known as interest. There are mainly two types of interest such as simple interest and compound interest. Application of simple interest is comparatively easier than applying compound interest. Compound interest can be further calculated with the help of simple interest as well. In this article, we will learn about simple interest and its applications.

Interest

Interest is an interesting concept. When we deposit the money for a period and withdraw it, we get an extra amount along with what we had deposited. Interest is that extra money paid by institutions such as banks, post offices on money deposited with them. In the same way, if we borrow money from a bank, a finance team, or a moneylender, we will have to pay back an extra amount than the amount we borrowed. This amount is also referred to as interest.

Simple Interest

Simple interest is an easy and basic method to calculate interest on money. In the simple interest method, interest always applies to the initial principal amount, with the interest of the same rate for every year. Before discussing the concept of simple interest, let’s first know the significance of a loan. Loans are sums of money that a person borrows from a bank or other institution to meet their financial obligations.

As an example of a loan, consider a home loan, a car loan, a student loan, or a personal loan. If the person borrows money, they must pay it back on time, plus a fee. This fee is usually the interest you pay on a loan.

Simple Interest: Formula

If interest is calculated uniformly on the original principal throughout the loan period, it is called simple interest. The simple interest formula is given by

\(S.I. = \frac{{P \times T \times R}}{{100}}\)
When \(P = \) Principal, \(R = \) Rate of interest per annum and \(T = \) time

The money borrowed initially is called the principal amount of the sum. It is known as the original sum also.
The amount is the total money that includes the principal and the interest paid by the borrower to the lender.
The interest of \(₹100\) for \(1\) year is known as the rate per annum.
Time is the period for which the sum is given to the borrower. It can be expressed in years, months, and days as well.

Simple Interest: Application

Car Loan

Car loans are paid monthly, which means that a part of the loan pays the remaining balance every month, and the balance portion goes toward the interest payment.
As the remaining loan balance reduces every month, the interest to be paid also decreases.
For example, suppose you have bought a car with a loan amount of \(₹300000.\) The loan rate of interest is \(5\% ,\) and the loan repayment time is \(5\) years.
Now, using the simple interest formula, you can easily calculate the monthly EMI of it. Let us find the total interest of \(5\) years on the principal amount.
\(S.I. = \frac{{P \times T \times R}}{{100}} \Rightarrow \frac{{300000 \times 5 \times 5}}{{100}} = ₹75000\)
Now, the amount \(= ₹300000 + ₹75000 = ₹375000\)
Thus, your EMI will be \( = \frac{{₹375000}}{{12 \times 5}} =₹ 6,250\)

Certificates of Deposit

It is a type of bank investment. The Certificate of Deposit (CD) is designed to pay you out a specific amount of money on a specific date.
Until that date arrives, you can’t take money out of a CD.

If you invested \(₹100000\) in \(1\) year at \(3\% \) interest yearly, the interest of \(1\) year on the principal amount.
\(S.I = \frac{ {P \times T \times R}}{ {100}} \Rightarrow \frac{ {100000 \times 12 \times 3}}{ {100 \times 12}} = ₹3000\)
Now, the amount \( =₹ 100000 + ₹3000 + ₹103000\)
So, you will get \(₹3000\) extra at the year-end.
If the CD pays the same interest rate per annum but only for three months, How much will you earn from CD?
\(S.I = \frac{ {P \times T \times R}}{ {100}} \Rightarrow \frac{ {100000 \times 3 \times 3}}{ {100 \times 12}} = ₹750\)
So, you will get \(₹750\) extra after three months of investment.

Consumer Loan

Generally, the department stores often provide appliances on a simple-interest basis for a maximum of one year.
For example, assume that you want to buy a refrigerator for \(₹20000\) and don’t have sufficient money to buy it in cash. So, you decided to buy it in a monthly instalment. The department store is giving the loan on \(8\% \) simple interest for \(12\) months or \(1\) year.
\(S.I = \frac{ {P \times T \times R}}{ {100}} \Rightarrow \frac{ {20000 \times 8 \times 12}}{ {100 \times 12}} = ₹1600\)
Now, the amount \(=₹ 20000 +₹ 1600 = ₹21600\)
So, you will pay \(₹1600\) extra at the year-end.
So, it is concluded that if you had \(₹20000\) then you would pay less amount instead of repaying a portion of it every month.

Currently, most banks apply compound interest to loans because it allows them to charge their customers a higher interest rate, but this method is more complex and challenging to explain. Using simple interest methods, on the other hand, simplifies the calculation. Simple interest is beneficial when a customer wants a loan for a short period, such as \(1\) month, \(2\) months, or \(6\) months.

Application of Simple Interest (SI) to Find the Compound Interest (CI)

The interest accrued during the first unit of time in compound interest is added to the original principal. The amount so found is taken as the principal for the second unit of time. The amount of this principal at the end of the second unit of the time becomes the principal of the third and so on.

The compound interest is the difference between the final amount and the original principal.
We will see how we could find the compound interest of a principal amount using the simple interest formula. In the table, we have taken the principal \(= ₹100\) at \(10\% \) per annum and for \(3\) years.

Solved Examples – Simple Interest and its Application

Q.1. An amount \(₹700\) is lent for one year at the rate of \(10\% \) per annum. Find the interest.
Ans: \(P = \) Principal \(₹700,\) \(R = \) Rate of Interest \( = 10\% \) per annum, \(T = \) Time \( = 1\)year
Then, \(S.I. = \frac{{P \times R \times T}}{{100}}\)
\( \Rightarrow S.I. = \frac{ {700 \times 10 \times 1}}{ {100}} = 70 = ₹70\)
Hence, the interest is \(₹70.\)

Q.2. Find the compound interest on \(₹12000\) for 3 years at \(10\% \) per annum compounded annually.
Ans: We know that the amount \(A\) at the end of \(n\) years at the rate of \(R\% \) per annum when the interest is compounded annually is given by \(A = P{\left({1 + \frac{R}{{100}}} \right)^n}\)
Here, \(P = ₹12000,R = 10\% \) per annum and \(n = 3\)
\(\therefore \) Amount \(A\) after \(3\) years \( = P{\left({1 + \frac{R}{{100}}} \right)^3}\)
\( =₹ 12000 {\left({1 + \frac{{10}}{ {100}}} \right)^3}\)
\( =₹ 12000 {\left({1 + \frac{{1}}{ {10}}} \right)^3}\)
\( =₹ 12000{\left({\frac{{11}}{{10}}} \right)^3}\)
\( =₹ 12000 \times \frac{ {11}}{ {10}} \times \frac{ {11}}{ {10}} \times \frac{{11}}{ {10}} =₹ 15972\)
Amount \( = ₹15972\)
\({\text{Compound}}\,{\text{Intrest}} = {\text{Amount}} -{\text{Principle}}\)
\({\text{Compound}}\,{\text{Intrest}} = ₹15972 – ₹12000 =₹ 3972\)
Hence, the compound interest is \(₹3972.\)

Q.3. Find the interest on \(₹1500\) at\(5\% \) per annum for 120 days.
Ans: \(P = ₹1500,R = 5\% \) per annum, \(T = 150\) days \( = \frac{{120}}{{365}}\) year \( = \frac{{24}}{{73}}\) year.
\(I = \frac{{P \times R \times T}}{{100}}\)
\(I = ₹\left({\frac{ {1500 \times 5 \times \frac{ {24}}{ {73}}}}{{100}}} \right) = ₹2,465.75\left({{\text{approximately}}} \right)\)
Hence, the interest is \( = ₹2,465.75\left({{\text{approximately}}} \right).\)

Q.4. What principal will amount \(₹900\) in 6 years at \(10\% \) simple interest?
Ans: We have, \(A = ₹900,T = 6\) years, \(R = 10\% \) per annum,
Let \(P\) be the principal and \(I\) be the interest.
Then, \(I = \frac{{P \times R \times T}}{{100}}\)
\( \Rightarrow I = \frac{{P \times 10 \times 6}}{{100}} = ₹\frac{{3P}}{5}\)
Now, \(A = P + I\)
\( \Rightarrow 900 = P + \frac{{3P}}{5}\)
\( \Rightarrow 900 = \frac{{5P + 3P}}{5}\)
\( \Rightarrow 900 = \frac{{8P}}{5}\)
\( \Rightarrow P = \frac{{900 \times 5}}{8} = 562.50\)
Hence, principal \(= ₹562.50\)

Q.5. \(₹8000\) is lent at \(5\% \) compound interest per year for 2 years. Find the amount and the compound interest.
Ans: For the first year:
Principal \(\left(P \right) = ₹8000;\) Rate \(\left( R \right) = 5\% \)
Time \(\left( T \right) = 1\) year
Interest \( = \frac{{P \times R \times T}}{{100}}\)
\(= \frac{ {₹8000 \times 5{\kern 1pt} \times 1}}{{100}} = ₹400\)
\({\text{Amount=Principal + Intrest}}\)
\( =₹ 8000 +₹ 400 =₹ 8400\)
According to the compound interest definition, the first year’s amount will work as principal for the next (second) year.
Therefore, for the second year:
Principal \(\left( P \right) = ₹8400\)
Rate \(\left( R \right) = 5\% \)
Time \(\left( T \right) = 1\) year
Interest \( =₹ \frac{{8400 \times 5{\kern 1pt} \times 1}}{{100}} = ₹420\) Amount at the end of the second year \(= ₹8400 + ₹420 =₹ 8820\)
Compound interest \( = \) Final Amount \( – \) Initial Principal
\(= ₹8820 – ₹8000 =₹ 820\)

Summary

This article will tell us about the definition of simple interest, simple interest formula, simple interest and compound interest, and application of simple interest. We have seen that we can find the compound interest using the simple interest formula. In the end, we solved examples on simple interest.

Frequently Asked Question (FAQs)

Frequently asked questions related to simple interest is listed as follows:

Q. What do you understand by simple interest?
Ans: Whenever a borrower takes out a loan from a lender, they promise to pay it back after a certain period. Besides the principal, the borrower must pay interest to the lender and the principal amount owed. The borrower and the lender agree on how to pay the interest. The deal is usually structured as a rate per unit of borrowed principal. In most cases, it’s a percentage of the principal per year. Rate per annum is the term used to describe the annual interest rate on a sum of \(100\) for a year.

Q. What is the formula of simple interest?
Ans: Simple interest is calculated using the formula
\(S.I. = \frac{{P \times T \times R}}{{100}}\)

Q. How do you find compound interest without formula?
Ans: Calculating compound interest without formulas can be done by repeating simple interest calculations with a growing principal.

Q. What is the application of simple interest in real life?
Ans: Generally, simple interest applies to car loans or short-term individual loans, consumer loans, certificates of deposits etc.

Q. How do you calculate compound interest directly without using simple interest formula?
Ans: We can calculate the compound interest by using the formula,
\(C.I. = P{\left( {1 + \frac{R}{{100}}} \right)^n} – P\)
Here, \(P=\) Principal, \(R=\) Rate of interest per annum and \(n=\) Number of years and \(A=\) Final amount.

We hope this detailed article on simple interest and its applications helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!